1.0 Converting. 1. What is the speed of a person walking at 3.1 mph in m/s? Show your work and box your answer (check your units)

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1 1.0 Converting There are 1, meters in one mile. One meter equals 3.28 feet. I mph equals m/s 1. What is the speed of a person walking at 3.1 mph in m/s? Show your work and box your answer (check your units) 2. What is the speed of a car traveling at 70 mph in m/s? Show your work and box your answer (check your units) 3. What is the speed of a plane traveling at 500 mph in m/s? Show your work and box your answer (check your units) 4. How many seconds are there in one hour? Show your work and box your answer (check your units) 1

2 Speed, Distance, and Acceleration 1.1 Motion is Relative 1. You are riding a bus traveling at 20m/s. You walk towards the back of the bus at 2 m/s relative to the bus. What is the magnitude of your velocity relative to the road in meters per second? Draw a picture Show your work and box your answer(s). Check your units! 2. You are riding a train traveling 50m/s. You walk towards the front of the train at 2 m/s relative to the train. What is the magnitude of your velocity relative to the tracks in meters per second? Draw a picture Show your work and box your answer(s). Check your units! 3. Car A is traveling at 27 m/s towards car B traveling at 51 m/s in the opposite direction. How fast does car A appear to be traveling to an observer in car B? Draw a picture Show your work and box your answer(s). Check your units! 2

3 4. A car A is traveling at a speed of 35 m/s and car B is traveling in the same direction at a speed of 38 m/s, both with respect to a fixed point on the road. How fast does car A appear to be traveling to an observer located in car B? Draw a picture Show your work and box your answer(s). Check your units! 5. A boat is traveling north. The people on the boat measure the water to be moving past the boat at a velocity of 5 m/s in the opposite direction to the south. A stationary viewer on the shore measures the velocity of the boat to be moving 2 m/s north. What is the actual velocity of the water as seen from the shore in meters per second? Draw a picture Show your work and box your answer(s). Check your units! 6. The takeoff speed of a military aircraft from an aircraft carrier is approximately 170 mi/hr relative to the air. They acquire this speed through a combination of a catapult system present on the aircraft carrier and the aircraft s jet propulsion system. A common strategy is to point the carrier and the plane into the wind. If a plane is taking off from an aircraft carrier that is moving at 40 mph into a 20 mph headwind, then what speed relative to the deck of the aircraft carrier must it obtain to takeoff? Show your work and box your answer(s). Check your units! 3

4 1.2 Finding Speed Average speed is equal to the total distance divided by the total time. Speed is a scaler quantity and only has magnitude. ave speed total distance total time 7. Jamaican sprinter Usain Bolt shocked the world by running the 100-meter dash in 9.58 seconds. Determine Usain s average speed in m/s and mph. s d 8. The world record in the mile run is 3:43 min. Find the average speed in both mph and in m/s? s d 4

5 9. In 2013 Danica Patrick made history by becoming the first NASCAR Sprint Cup female driver to win the pole position and she also recorded the fastest qualifying speed ever at Daytona International Speedway in Daytona Beach, Florida. Danica had an average qualifying time of sec per lap on the 2.5-mile (4, m) track. What was Danica s average speed in mph and m/s? s d 10. A monkey watches a thunderstorm from his back porch. He sees a flash lightning off in the distance and begins counting the seconds until he hears the clap of thunder 5 seconds later. Assume that the speed of sound in air is 340 m/s. How far away was the lightning bolt in both meters and in miles? s d 5

6 11. In 2008 Doc Fizzix drove home from New Orleans to Round Rock, Tx in record time. It took only 4.75 hours to make the trip home and he average mph (48.09 m/s); and that was even after making three stops along the way. From the information given, what is the total distance from Round Rock, TX to New Orleans, LA in miles? s d 12. An echo is caused by a sound wave that travels away from a source, hits a target, and then bouncing back to the original source. If you stand at the rim of the Grand Canyon and yell down towards the bottom, your echo will bounce back from the canyon floor 5.20 s later. Assume that the speed of sound in air is m/s. What is the total distance the sound wave traveled and how deep is the Grand Canyon at this location? Find both answers in meters and miles. s d 6

7 13. Not only can ants lift 20 times their own body weight, but their body structure and musculature allow them to run very quickly for their size. Their six legs propel them to an average speed of mph (0.083 m/s), how long would it take an ant to run the 100-meter dash in seconds and in hours? Show your work and box your answer s d Draw a picture 14. A baseball pitcher throws a baseball at 100 mph (44.70 m/s) a distance of ft (18.39 m) to the catcher. How much time does the batter have to react to the pitch? s d Show your work and box your answer Draw a picture 7

8 1.3 Velocity, Distance, and Displacement The total distance is the sum of all the distances traveled. The total distance is not a vector so direction in not important, use the absolute value only. Change in distance (displacement) is a vector quantity. The change in distance (displacement) is the difference from where you start to where you end up, direction is important. d Total d 1 + d Δd d f d o The average velocity is equal to the change in distance divided by the change in time. Velocity is a vector quantity and has magnitude with direction. v Δd Δt As appropriate use up, down, north, south, east, and/or west for the following. 15. A girl leaves a history classroom and walks 10 meters north to a drinking fountain. Then she turns and walks 30 meters south to her art classroom. What is the girl s total displacement from her history classroom in meters? What formula(s) are you using? Show your work and box your answer 16. A bird flies west for 8.5 kilometers and east for 3 kilometers, and then turns around and heads back west for 2 kilometers. What is the total distance and b) the total displacement of the bird? Find both in kilometers? What formula(s) are you using? Show your work and box your answer b) 8

9 17. A person travels 23 meters north in 16 sec, 5 meters south in 4 sec, and 16 meters north in 18 sec. What was the total distance traveled and b) the total displacement? What formula(s) are you using? Show your work and box your answer b) 18. A monkey travels 30 miles (48.28 kilometers) north in 20 min, then 25 miles (40.23 kilometers) south in 45 min. What is the monkey s average speed and b) the average velocity in m/s? What formula(s) are you using? Show your work and box your answer b) 19. A ball shot into the air travels to a maximum height of 20 meters and then falls back to the release point in 4 seconds. What was the average speed of the ball and b) the average velocity of the ball in meters per second? What formula(s) are you using? Show your work and box your answer b) 9

10 1.4 Acceleration Average acceleration is the change in velocity over time. It is the rate at which velocity is changing. Change in velocity is a vector quantity. The change in velocity is the difference from where you start to where you end up, direction is important. Δv v o a Δv Δt 20. The average car in the United States will go from 0-60 mph (26.82 m/s) in 9 seconds. What is the magnitude of the acceleration in mph/s and m/s 2? a 21. A Porsche 911, driven by a monkey goes from 0-60 mph (26.82 m/s in 3.7 seconds. What is the magnitude of the acceleration in mph/s and m/s 2? a 10

11 22. A car initially traveling at a velocity of 55 mph (24.59 m/s) north accelerates uniformly to a speed of 70 mph (31.29 m/s) north in 10 seconds. What is the magnitude and direction of the car s acceleration in mph/s and m/s 2? a b) 23. A Porsche 911 is heading north at 60 mph (26.82 m/s) when the brakes are applied causing the car to come to rest in 2.32 seconds. What is the magnitude and direction of the car s acceleration in mph/s and m/s 2? a b) 11

12 24. A monkey, riding on a bike, is traveling at 9.6 m/s north when he accelerates at a rate of 3.2 m/s 2. What is the instantaneous velocity of monkey after 2.5 second? b) What is the velocity of the monkey after another 2.5 seconds (5 seconds total)? a b) 25. A car, heading north, decelerates at a rate of 3.8 m/s 2 for 12 seconds. The car s initial speed was 60 mph (26.82 m/s). What was the car s final velocity? a 12

13 26. The head of a rattlesnake can accelerate at 50 m/s 2 as it strikes a victim. If a car could have the same acceleration as a rattlesnake, how much time would it take for the car to go from 0-60 mph (26.82 m/s)? a 27. The brakes on the average automobile are capable of accelerations of 5.18 m/s 2. If you are traveling at 80 mph (35.76 m/s) when you suddenly see a state trooper on the highway, how much time will it take to slow a car down to the speed limit of 65 mph (29.06 m/s)? a 13

14 1.5 Kinematics Kinematics puts it all together, distance, velocity, acceleration, and time. Choose equation 1-5 based on the variable that you are missing from your givens. Missing Equation 1 v o + aδt Δd Equation 2 Δd (v o + v 2 ) 2 Δt Equation 3 Δd v o Δt a(δt)2 Equation 4 2 v o 2 + 2aΔd t a 28. A racecar starting from rest and accelerates uniformly towards the east at a rate of 4.90 m/s 2. What is the car s velocity after it has traveled 200-meters? a Δd 14

15 29. A car is initially traveling east with a speed of 5.0 m/s accelerates uniformly at 2.0 m/s 2 towards the east for 10 seconds along a straight line. During this 10-second interval, what is the magnitude and direction of the cars displacement? a Δd 30. A monkey on a skateboard increases his speed uniformly from 2.0 m/s to 7.0 m/s over a distance of 12 meters. What is the magnitude and direction of the monkey s acceleration? a Δd 15

16 31. A car initially traveling at a speed of 16 m/s accelerates uniformly to a speed of 20- m/s over a distance of 36 meters. What is the magnitude of the car s acceleration? b) How long does this take? a Δd b) 32. A formula 1 racer can go from mph in 4 seconds ( m/s). What is the magnitude of the acceleration and, assuming the acceleration remains constant, b) how fast will the car be traveling after 7 second? a Δd b) 16

17 1.6 Free-Fall Use 9.8 m/s/s for gravity when needed. Make objects moving towards the Earth positive and away negative. 33. A monkey is standing under a coconut tree when a coconut falls from the tree and lands on his head. If the time of fall was 1.8 s, how fast was the nut falling when it hit the monkey on the head? g Δh 34. A baseball dropped from the top of a building takes 3.1 seconds to hit the ground. How fast is the ball traveling when it hits the ground? b) How tall is the building? g Δh 17

18 35. You are on the observation deck of the UT Tower at the University of Texas campus. You want to get a rough estimate of how high up you are so you drop a quarter from the observation deck and count how many seconds it takes before for the quarter to hit the ground. Your count gives you a time of 4 seconds. How high up are you? b) What is the velocity of the coin as it hits the ground? g Δh 36. Daredevil Dave waves to the crowd and then jumps off of a 120m high bridge without first attaching the bungee cord. How long does Dave have to think about his error? g Δh 18

19 37. You drop a penny from the observation deck located on the 102nd floor of the Empire State building in New York City 1,250 ft (381 m) above the ground. How long does it take the penny to hit the ground and b) how fast is the penny falling when it does hit the ground? g Δh b) 38. A raindrop falls to the Earth from a cloud 1,700 m above the Earth s surface. If the raindrop was not slowed by air resistance how fast would the raindrop be falling by the time it hit the ground? g Δh 19

20 39. A ball is thrown towards the ground from a window 50 m above the ground with an initial speed of 10.0 m/s. How fast will the ball be traveling when it hits the ground? b) How long does it take for the ball to hit the ground? g Δh b) 40. A ball is thrown towards the ground with an initial speed of 20 m/s and hits the ground traveling m/s. How far did the ball fall? g Δh 20

21 41. A bowling ball falls freely from rest on a planet where g 6 m/s 2. How far does it fall in 4 seconds and b) how fast is it moving? g Δh b) 42. An astronaut standing on a platform on the Moon drops a hammer. If the hammer falls 6.0 meters vertically in 2.7 seconds, what is its acceleration of gravity on the moon? g Δh 21

22 1.7 Going-Up 43. A ball is thrown vertically upward and takes 3-seconds to reach its highest point. What was the initial speed of the ball? b) How long was the ball in the air total? g Δh b) 44. Michael Jordan has a hang-time of 0.98 seconds (up and down). How fast does he need to leave the ground in order to attain this time and b) how high does he go? g Δh b) 22

23 45. At the beginning of a basketball game, a referee tosses the ball straight up with a speed of 4.6 m/s. A player cannot touch the ball until after it reaches its max height. What is the minimum time that a player must wait before touching the ball. g Δh 46. A bullet is fired from a gun pointed straight up into the air with a muzzle speed of 460 m/s. How long does it take the bullet to reach it s highest point and b) how high does the bullet rise above the gun? g Δh b) 23

24 47. At what speed do you have to throw a ball into the air in order to reach a height of 50 meters? g Δh 48. A basketball player jumped straight up to grab a rebound. If she was in the air for a total of 0.80 second (up and down), how high did she jump? g Δh 24

25 49. Former NBA player, Spudd Webb, has an impressive vertical jump of 1.22 meters. What velocity is needed to reach this height and b) what is the total hang time? g Δh b) 50. Girl throws a ball vertically from the top of a 12-m high building. The ball hits the ground 0.8 s later. With what speed and in what direction was the ball thrown? g Δh 25