problem solving exercises in physics answers pdf

Problems & Exercises

1.2 physical quantities and units.

The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

A car is traveling at a speed of 33 m/s 33 m/s size 12{"33"" m/s"} {} . (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h 90 km/h size 12{"90"" km/h"} {} speed limit?

Show that 1 . 0 m/s = 3 . 6 km/h 1 . 0 m/s = 3 . 6 km/h size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {} . Hint: Show the explicit steps involved in converting 1 . 0 m/s = 3 . 6 km/h. 1 . 0 m/s = 3 . 6 km/h. size 12{1 "." 0`"m/s"=3 "." "6 km/h"} {}

American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)

What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)

Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.)

The speed of sound is measured to be 342 m/s 342 m/s size 12{"342"" m/s"} {} on a certain day. What is this in km/h?

Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

(a) Refer to Table 1.3 to determine the average distance between the Earth and the Sun. Then calculate the average speed of the Earth in its orbit in kilometers per second. (b) What is this in meters per second?

1.3 Accuracy, Precision, and Significant Figures

Express your answers to problems in this section to the correct number of significant figures and proper units.

Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

(a) A car speedometer has a 5.0 % 5.0 % size 12{5.0%} {} uncertainty. What is the range of possible speeds when it reads 90 km/h 90 km/h size 12{"90"" km/h"} {} ? (b) Convert this range to miles per hour. 1 km = 0.6214 mi 1 km = 0.6214 mi size 12{"1 km" "=" "0.6214 mi"} {}

An infant’s pulse rate is measured to be 130 ± 5 130 ± 5 size 12{"130" +- 5} {} beats/min. What is the percent uncertainty in this measurement?

(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

A can contains 375 mL of soda. How much is left after 308 mL is removed?

State how many significant figures are proper in the results of the following calculations: (a) 106 . 7 98 . 2 / 46 . 210 1 . 01 106 . 7 98 . 2 / 46 . 210 1 . 01 size 12{ left ("106" "." 7 right ) left ("98" "." 2 right )/ left ("46" "." "210" right ) left (1 "." "01" right )} {} (b) 18 . 7 2 18 . 7 2 size 12{ left ("18" "." 7 right ) rSup { size 8{2} } } {} (c) 1 . 60 × 10 − 19 3712 1 . 60 × 10 − 19 3712 size 12{ left (1 "." "60" times "10" rSup { size 8{ - "19"} } right ) left ("3712" right )} {} .

(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

(a) If your speedometer has an uncertainty of 2 . 0 km/h 2 . 0 km/h size 12{2 "." 0" km/h"} {} at a speed of 90 km/h 90 km/h size 12{"90"" km/h"} {} , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h 60 km/h size 12{"60"" km/h"} {} , what is the range of speeds you could be going?

(a) A person’s blood pressure is measured to be 120 ± 2 mm Hg 120 ± 2 mm Hg size 12{"120" +- 2" mm Hg"} {} . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg 80 mm Hg size 12{"80"" mm Hg"} {} ?

A person measures his or her heart rate by counting the number of beats in 30 s 30 s size 12{"30"" s"} {} . If 40 ± 1 40 ± 1 size 12{"40" +- 1} {} beats are counted in 30 . 0 ± 0 . 5 s 30 . 0 ± 0 . 5 s size 12{"30" "." 0 +- 0 "." 5" s"} {} , what is the heart rate and its uncertainty in beats per minute?

What is the area of a circle 3 . 102 cm 3 . 102 cm size 12{3 "." "102"" cm"} {} in diameter?

If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?

A marathon runner completes a 42 . 188 -km 42 . 188 -km size 12{"42" "." "188""-km"} {} course in 2 h 2 h size 12{2" h"} {} , 30 min, and 12 s 12 s size 12{"12"" s"} {} . There is an uncertainty of 25 m 25 m size 12{"25"" m"} {} in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

The sides of a small rectangular box are measured to be 1 . 80 ± 0 . 01 cm 1 . 80 ± 0 . 01 cm size 12{1 "." "80" +- 0 "." "01"" cm"} {} , {} 2 . 05 ± 0 . 02 cm, and 3 . 1 ± 0 . 1 cm 2 . 05 ± 0 . 02 cm, and 3 . 1 ± 0 . 1 cm size 12{2 "." "05" +- 0 "." "02"" cm, and 3" "." 1 +- 0 "." "1 cm"} {} long. Calculate its volume and uncertainty in cubic centimeters.

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm = 0 . 4539 kg 1 lbm = 0 . 4539 kg size 12{1" lbm"=0 "." "4539"`"kg"} {} . (a) If there is an uncertainty of 0 . 0001 kg 0 . 0001 kg size 12{0 "." "0001"`"kg"} {} in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

The length and width of a rectangular room are measured to be 3 . 955 ± 0 . 005 m 3 . 955 ± 0 . 005 m size 12{3 "." "955" +- 0 "." "005"" m"} {} and 3 . 050 ± 0 . 005 m 3 . 050 ± 0 . 005 m size 12{3 "." "050" +- 0 "." "005"" m"} {} . Calculate the area of the room and its uncertainty in square meters.

A car engine moves a piston with a circular cross section of 7 . 500 ± 0 . 002 cm 7 . 500 ± 0 . 002 cm size 12{7 "." "500" +- 0 "." "002"`"cm"} {} diameter a distance of 3 . 250 ± 0 . 001 cm 3 . 250 ± 0 . 001 cm size 12{3 "." "250" +- 0 "." "001"`"cm"} {} to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

1.4 Approximation

How many heartbeats are there in a lifetime?

A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?

How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10 − 22  s 10 − 22  s size 12{"10" rSup { size 8{ - "22"} } " s"} {} .)

Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10 − 27  kg 10 − 27  kg size 12{"10" rSup { size 8{ - "27"} } " kg"} {} and the mass of a bacterium is on the order of 10 − 15  kg. 10 − 15  kg. size 12{"10" rSup { size 8{ - "15"} } "kg"} {} )

Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?

(a) What fraction of Earth’s diameter is the greatest ocean depth? (b) The greatest mountain height?

(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?

Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?

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Example Physics Problems and Solutions

Learning how to solve physics problems is a big part of learning physics. Here’s a collection of example physics problems and solutions to help you tackle problems sets and understand concepts and how to work with formulas:

Physics Homework Tips Physics homework can be challenging! Get tips to help make the task a little easier.

Unit Conversion Examples

There are now too many unit conversion examples to list in this space. This Unit Conversion Examples page is a more comprehensive list of worked example problems.

Newton’s Equations of Motion Example Problems

Equations of Motion – Constant Acceleration Example This equations of motion example problem consist of a sliding block under constant acceleration. It uses the equations of motion to calculate the position and velocity of a given time and the time and position of a given velocity.

Equations of Motion Example Problem – Constant Acceleration This example problem uses the equations of motion for constant acceleration to find the position, velocity, and acceleration of a breaking vehicle.

Equations of Motion Example Problem – Interception

This example problem uses the equations of motion for constant acceleration to calculate the time needed for one vehicle to intercept another vehicle moving at a constant velocity.

Vertical Motion Example Problem – Coin Toss Here’s an example applying the equations of motion under constant acceleration to determine the maximum height, velocity and time of flight for a coin flipped into a well. This problem could be modified to solve any object tossed vertically or dropped off a tall building or any height. This type of problem is a common equation of motion homework problem.

Projectile Motion Example Problem This example problem shows how to find different variables associated with parabolic projectile motion.

Accelerometer and Inertia Example Problem Accelerometers are devices to measure or detect acceleration by measuring the changes that occur as a system experiences an acceleration. This example problem uses one of the simplest forms of an accelerometer, a weight hanging from a stiff rod or wire. As the system accelerates, the hanging weight is deflected from its rest position. This example derives the relationship between that angle, the acceleration and the acceleration due to gravity. It then calculates the acceleration due to gravity of an unknown planet.

Weight In An Elevator Have you ever wondered why you feel slightly heavier in an elevator when it begins to move up? Or why you feel lighter when the elevator begins to move down? This example problem explains how to find your weight in an accelerating elevator and how to find the acceleration of an elevator using your weight on a scale.

Equilibrium Example Problem This example problem shows how to determine the different forces in a system at equilibrium. The system is a block suspended from a rope attached to two other ropes.

Equilibrium Example Problem – Balance This example problem highlights the basics of finding the forces acting on a system in mechanical equilibrium.

Force of Gravity Example This physics problem and solution shows how to apply Newton’s equation to calculate the gravitational force between the Earth and the Moon.

Coupled Systems Example Problems

Coupled systems are two or more separate systems connected together. The best way to solve these types of problems is to treat each system separately and then find common variables between them. Atwood Machine The Atwood Machine is a coupled system of two weights sharing a connecting string over a pulley. This example problem shows how to find the acceleration of an Atwood system and the tension in the connecting string. Coupled Blocks – Inertia Example This example problem is similar to the Atwood machine except one block is resting on a frictionless surface perpendicular to the other block. This block is hanging over the edge and pulling down on the coupled string. The problem shows how to calculate the acceleration of the blocks and the tension in the connecting string.

Friction Example Problems

These example physics problems explain how to calculate the different coefficients of friction.

Friction Example Problem – Block Resting on a Surface Friction Example Problem – Coefficient of Static Friction Friction Example Problem – Coefficient of Kinetic Friction Friction and Inertia Example Problem

Momentum and Collisions Example Problems

These example problems show how to calculate the momentum of moving masses.

Momentum and Impulse Example Finds the momentum before and after a force acts on a body and determine the impulse of the force.

Elastic Collision Example Shows how to find the velocities of two masses after an elastic collision.

It Can Be Shown – Elastic Collision Math Steps Shows the math to find the equations expressing the final velocities of two masses in terms of their initial velocities.

Simple Pendulum Example Problems

These example problems show how to use the period of a pendulum to find related information.

Find the Period of a Simple Pendulum Find the period if you know the length of a pendulum and the acceleration due to gravity.

Find the Length of a Simple Pendulum Find the length of the pendulum when the period and acceleration due to gravity is known.

Find the Acceleration due to Gravity Using A Pendulum Find ‘g’ on different planets by timing the period of a known pendulum length.

Harmonic Motion and Waves Example Problems

These example problems all involve simple harmonic motion and wave mechanics.

Energy and Wavelength Example This example shows how to determine the energy of a photon of a known wavelength.

Hooke’s Law Example Problem An example problem involving the restoring force of a spring.

Wavelength and Frequency Calculations See how to calculate wavelength if you know frequency and vice versa, for light, sound, or other waves.

Heat and Energy Example Problems

Heat of Fusion Example Problem Two example problems using the heat of fusion to calculate the energy required for a phase change.

Specific Heat Example Problem This is actually 3 similar example problems using the specific heat equation to calculate heat, specific heat, and temperature of a system.

Heat of Vaporization Example Problems Two example problems using or finding the heat of vaporization.

Ice to Steam Example Problem Classic problem melting cold ice to make hot steam. This problem brings all three of the previous example problems into one problem to calculate heat changes over phase changes.

Charge and Coulomb Force Example Problems

Electrical charges generate a coulomb force between themselves proportional to the magnitude of the charges and inversely proportional to the distance between them. Coulomb’s Law Example This example problem shows how to use Coulomb’s Law equation to find the charges necessary to produce a known repulsive force over a set distance. Coulomb Force Example This Coulomb force example shows how to find the number of electrons transferred between two bodies to generate a set amount of force over a short distance.

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Physics Problems with Solutions

• Electric Circuits
• Electrostatic
• Calculators
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• Uniform Acceleration Motion: Problems with Solutions

Problems on velocity and uniform acceleration are presented along with detailed solutions and tutorials can also be found in this website.

From rest, a car accelerated at 8 m/s 2 for 10 seconds. a) What is the position of the car at the end of the 10 seconds? b) What is the velocity of the car at the end of the 10 seconds? Solution to Problem 1

With an initial velocity of 20 km/h, a car accelerated at 8 m/s 2 for 10 seconds. a) What is the position of the car at the end of the 10 seconds? b) What is the velocity of the car at the end of the 10 seconds? Solution to Problem 2

A car accelerates uniformly from 0 to 72 km/h in 11.5 seconds. a) What is the acceleration of the car in m/s 2 ? b) What is the position of the car by the time it reaches the velocity of 72 km/h? Solution to Problem 3

An object is thrown straight down from the top of a building at a speed of 20 m/s. It hits the ground with a speed of 40 m/s. a) How high is the building? b) How long was the object in the air? Solution to Problem 4

A train brakes from 40 m/s to a stop over a distance of 100 m. a) What is the acceleration of the train? b) How much time does it take the train to stop? Solution to Problem 5

A boy on a bicycle increases his velocity from 5 m/s to 20 m/s in 10 seconds. a) What is the acceleration of the bicycle? b) What distance was covered by the bicycle during the 10 seconds? Solution to Problem 6

a) How long does it take an airplane to take off if it needs to reach a speed on the ground of 350 km/h over a distance of 600 meters (assume the plane starts from rest)? b) What is the acceleration of the airplane over the 600 meters? Solution to Problem 7

Starting from a distance of 20 meters to the left of the origin and at a velocity of 10 m/s, an object accelerates to the right of the origin for 5 seconds at 4 m/s 2 . What is the position of the object at the end of the 5 seconds of acceleration? Solution to Problem 8

What is the smallest distance, in meters, needed for an airplane touching the runway with a velocity of 360 km/h and an acceleration of -10 m/s 2 to come to rest? Solution to Problem 9

Problem 10:

To approximate the height of a water well, Martha and John drop a heavy rock into the well. 8 seconds after the rock is dropped, they hear a splash caused by the impact of the rock on the water. What is the height of the well. (Speed of sound in air is 340 m/s). Solution to Problem 10

Problem 11:

A rock is thrown straight up and reaches a height of 10 m. a) How long was the rock in the air? b) What is the initial velocity of the rock? Solution to Problem 11

Problem 12:

A car accelerates from rest at 1.0 m/s 2 for 20.0 seconds along a straight road . It then moves at a constant speed for half an hour. It then decelerates uniformly to a stop in 30.0 s. Find the total distance covered by the car. Solution to Problem 12

More References and links

• Velocity and Speed: Tutorials with Examples
• Velocity and Speed: Problems with Solutions
• Acceleration: Tutorials with Examples
• Uniform Acceleration Motion: Equations with Explanations

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Ray Optics: Reflection and Mirrors

Calculator pad, version 2, reflection and mirrors: problem set.

A light ray approaches a mirror at an angle of incidence of 25°. What is the angle of reflection?

• Audio Guided Solution
• Show Answer

A light ray approaches a mirror at an angle of 22° with the mirror surface. What is the angle of reflection of this light ray?

Angle B = 38° Angle C = 52° Angle D = 38°

Anna Litical is doing the Plane Mirror Lab in physics class. She places a pin a distance of 4.9 cm from a plane mirror. How far behind the mirror can the image be expected to appear?

Baldwin Young stands 68 cm from his dresser mirror, inspecting his scalp. How far is the image of his scalp located from his scalp?

A meter stick (object) is placed in an upright position in front of a plane mirror as shown in the diagram at the right. The image of the meter stick is equidistant from the mirror. Suppose that the meter stick is equipped with a working eyeball capable of viewing the top and the bottom of its image. The eyeball is located at the 90-cm mark on the meter stick. Using either a ray diagram or geometry, determine … a. … the location of the intersection of the eye's line of sight with the mirror as the eyeball sights at the top of the image. b. … the location of the intersection of the eye's line of sight with the mirror as the eyeball sights at the bottom of the image. c. … the amount of mirror required by the meter stick to view the image.

a. 95 cm b. 45 cm c. 50 cm

A spherical concave mirror has a radius of curvature of +62 cm. What is the focal length of the mirror?

A decorative garden sphere has a diameter of 44 cm. The reflecting surface of the shiny sphere makes a great convex mirror. What is the focal point of the convex surface?

In a physics demonstration, a concave mirror having a 50.0 cm focal length is used to create images of a candle located at various locations along its principal axis. Beginning from a distance of several meters from the mirror, a candle is moved forward and its image is projected onto an opaque screen. Determine the image distances (distance from mirror to image) for object distances (distance from object to mirror) of … a. … 125.0 cm b. … 100.0 cm c. … 75.0 cm d. … 50.0 cm (Be careful with your math; the result is surprising.) e. … 25.0 cm

a. 83.3 cm b. 100.0 cm c. 150.0 cm d. No image. A solution to the mirror equation does not exist for this object distance. e. -50.0 cm

Problem 10:

Obtaining a large spherical mirror with a focal length of 0.654 m from the Physics Storeroom, Mr. H takes his last period class outside for a fascinating demo. A student volunteer holds the mirror at an angle such that the face of the mirror is directed towards the Sun - roughly 1.46x10 11 m away. Mr. H then uses a piece of paper with George Washington's picture on it to focus the image of the sun on the sheet of paper. Before the paper engulfs in flames, a bright image of the sun can be seen on the paper. Use the mirror equation to calculate the distance from the mirror to the image of the sun.

Problem 11:

Every morning Bob Gillette uses a shaving mirror with a focal length of 72 cm to view the image of his face. Supposing his face is 18 cm from the mirror, determine the image distance and the magnification of his face.

d i = -24 cm Magnification = 1.33

Problem 12:

The infamous Chinese magician Foo Ling Yu places a 56-mm tall light bulb a distance of 124 cm from a spherical concave mirror with a focal length of 62 cm. a. Determine the image distance and image height. b. Describe the orientation and type of the image.

a. d i = 124 cm and h i = -56 mm b. The image is inverted and real.

Problem 13:

In a physics lab, Anna Litical and Noah Formula position a small night light bulb at several locations along the principal axis of a concave mirror. Using a note card, they locate the image of the light bulb. The mirror has a focal length of 32.0 cm. What image distances would you expect Anna and Noah to observe when the object is located at distances of … a. … 85.3 cm from the mirror? b. … 64.0 cm from the mirror? c. … 48.1 cm from the mirror?

a. 51.2 cm b. 64.0 cm c. 95.6 cm

Problem 14:

Ima Primpin uses a cosmetic mirror to magnify her eyelashes during the traditional morning painting session. Her 1.2-cm long eyelashes are magnified to 1.6 cm when placed 5.8 cm from the mirror. a. Determine the image distance for such an upright image. b. Determine the focal length of the mirror.

a. -7.7 cm b. 23.2 cm

Problem 15:

In the Fall of 2006, the Sky Mirror sculpture was opened in Rockefeller Center in New York City. Standing three stories tall and weighing 23 tons, its concave side faced the Rockefeller Center and its convex side faced Fifth Avenue. a. A taxi on Fifth Avenue is located 38 m from the convex side of the sculpture and its image is one-fifth the size of the taxi. Determine the focal length of the mirror. b. Estimate the image size and image distance of the 260-m tall Rockefeller Center if it is located an estimated distance of 95 meters from the concave mirror surface. Assume the focal length of the concave side is the same magnitude as the focal length of the convex side.

a. -9.5 m b. d i = 11 m (rounded from 10.55 m) and h i = -29 m (- indicates inverted image)

Problem 16:

A convex spherical mirror has a focal point located a distance of 24.6 cm from the surface of the mirror. (You will have to decide for yourself whether f is + or -.) a. Find the image distance (in cm) for an object distance of 76.8 cm. b. Determine the magnification of this image.

a. d i = -18.6 cm b. M = 0.243

Problem 17:

A convenient store mounts a convex mirror in the corner of the store to serve as a security mirror and reduce the frequency of five-finger discounts . When Robin Storz is positioned a distance of 4.8 m from the mirror, her image is magnified by a factor of one-half. Determine the focal length of the mirror.

Problem 18:

Kerry Uss is studying the convex side of her soup spoon. She notices that her 3.8-cm tall nose appears to be 1.2 cm tall when positioned a distance of 2.4 cm from the spoon. a. Determine the image distance for this particular object distance. b. Determine the focal length of the convex side of the spoon.

a. d i = -0.76 cm b. f = -1.1 cm

Problem 19:

A large spherical mirror sculpture is constructed in the town square at Physicston, Illinois. The sculpture consists of a large sphere with a diameter of 24 meters which is coated with a reflecting material. A 1.8 meter tall photographer stands a distance of 38 m from the concave side of the sculpture and takes a picture. Determine the image distance and the magnification of the photographer.

d i = 7.1 m Mag = -0.19

Problem 20:

Baxter Nachure lives in the country along Sinewave road. It is difficult to pull out of the driveway onto the road since the road is curved and trees prevent him from seeing around the corner. He recently installed a large convex mirror at one of the curves to give him a wider angle of view. It has a focal length of -1.54 meters. Determine the magnification of an oncoming car located 35.8 m from the mirror.

Problem 21:

A virtual image is formed 26.9 cm from a concave mirror having a radius of curvature of 48.1 cm. Determine the object distance.

Problem 22:

An 4.9-cm tall object is positioned 14.8 cm from a mirror. Determine the radius of curvature which the mirror must have in order to produce an upright image that is 7.2 cm tall?

Problem 23:

A dentist uses a spherical mirror to produce an upright image of a patient's tooth which is magnified by a factor of 4.5 when placed 1.8 cm from the tooth. (a) What type of mirror - concave or convex - is being used? (b) What is the focal length of the mirror?

a. Concave mirror. Convex mirrors do not magnify the image; they only reduce the image. b. 2.3 cm

Problem 24:

The real image produced by a concave mirror is observed to be six times larger than the object when the object is 34.2 cm in front of a mirror. Determine the radius of curvature of this mirror.

Problem 25:

A shiny bauble (ornament) hangs on Mr. H's Christmas tree. The bauble has a radius of 4.8 cm. Matthew looks into the bauble and observes an image of his face which is one-eighth the size of his face. How far from the bauble is Matthew's face?

Problem 26:

A child at an amusement park stands in front of a concave mirror with a focal length of 73.9 cm. With great amusement, the child holds her cotton candy close to the mirror and observes that its image is magnified by a factor of five. Determine the object distance which creates this magnification of five.

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