Physics problems: kinematics Part 1 Problem 1. A train covers 60 miles between 2 p.m. and 4 p.m. How fast was it going at 3 p.m.? Problem 2. Is it possible that the car could have accelerated to 55mph within 268 meters if the car can only accelerate from 0 to 60 mph in 15 seconds?
Problem 3. A car travels up a hill at a constant speed of 37 km/h and returns down the hill at a constant speed of 66 km/h. Calculate the average speed for the whole trip.
Problem 4. An archer shoots an arrow with a velocity of 30 m/s at an angle of 20 degrees with respect to the horizontal. An assistant standing on the level ground 30 m downrange from the launch point throws an apple straight up with the minimum initial speed necessary to meet the path of the arrow. What is the initial speed of the apple and at what time after the arrow is launched should the apple be thrown so that the arrow hits the apple?
Problem 5. A box sits on a horizontal wooden board. The coefficient of static friction between the box and the board is 0.5. You grab one end of the board and lift it up, keeping the other end of the board on the ground. What is the angle between the board and the horizontal direction when the box begins to slide down the board?
Problem 6. A 8 kg block is at rest on a horizontal floor. If you push horizontally on the 8 kg block with a force of 20 N, it just starts to move. (a) What is the coefficient of static friction? (b) A 10.0 kg block is stacked on top of the 8 kg block. What is the magnitude F of the force, acting horizontally on the 8 kg block as before, that is required to make the two blocks start to move?
Problem 7. A car is accelerating at
. Find its acceleration in
.
Problem 8. We drive a distance of 1 km at 16 km/h. Then we drive an additional distance of 1 km at 32 km/h. What is our average speed?
Problem 9. An airliner reaches its takeoff speed of 163 mph in 36.2 s. What is the magnitude of its average acceleration.
Problem 10. A car is initially traveling due north at 23 m/s. (a) Find the velocity of the car after 4 s if its acceleration is due north. (b) Find the velocity of the car after 4 s if its acceleration is instead due south. Problem 11. From the dimensional analysis find the time t it takes for a ball to fall from a height h.
Problem 12. You are driving along the street at the speed limit (35mph) and 50 meters before reaching a traffic light you notice it becoming yellow. You accelerate to make the traffic light within the 3 seconds it takes for it to turn red. What is your speed as you cross the intersection? Assume that the acceleration is constant and that there is no air resistance.
Problem 13. How high can a human throw a ball if he can throw it with initial velocity 90 mph.
Problem 14. Mr. Letourneau is flying his broom stick parallel to the ground. He undergoes two consecutive displacements. The first is 100 km 10 degrees west of north, and the second is 120 km 50 degrees east of north. What is the magnitude of the broom stick's displacement? Problem 15. In reaching her destination, a backpacker walks with an average velocity of 1 m/s, due west. This average velocity results, because she hikes for 6 km with an average velocity of 3 m/s due west, turns around, and hikes with an average velocity of 0.3 m/s due east. How far east did she walk (in kilometers)?
Problem 16. It takes you 9.5 minutes to walk with an average velocity of 1.2 m/s to the north from the bus stop to museum entrance. What is your displacement? Problem 17.
What is 3.3 slug in kilograms?
Problem 18. An athlete swims the length of a 50.0-m pool in 20.0s and makes the return trip to the starting position in 22.0s. Determine her average velocities in (a) the first half of the swim, (b) the second half of the swim, and (c) the round trip. Problem 19. A speedboat increases its speed uniformly from 20 m/s to 30 m/s in a distance of 200m. Find (a) the magnitude of its acceleration and (b) the time it takes the boat to travel the 200-m distance. Problem 20. The car drives straight off the edge of a cliff that is 57 m high. The investigator at the scene of the accident notes that the point of impact is 130 m from the base of the cliff. How fast was the car traveling when it went over the cliff? Problem 21. An aircraft has a lift-off of 120km/h. (a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240m? (b) How long does it take the aircraft to become airborne? Problem 22. A ball is thrown vertically upward with a speed of 25.0m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started? Problem 23.
A tortoise and a hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000 meters at a speed of 0.2 m/s. The rabbit runs the first 200 meters at 2 m/s, stops to take a nap for 1.3 hours, and awakens to finish the last 800 meters with an average speed of 3 m/s. Who wins the race and by how much time?
Problem 24. The slowest animal ever discovered is a crab found in the Red Sea that travels an average speed of 5.7 km/year. How long will it take this crab to travel 1 meter? Problem 25. A "moving sidewalk" in a busy airport terminal moves 1 m/s and is 200 m long. A passenger steps onto one end and walks, in the same direction as the sidewalk is moving, at a rate of 2.0 m/s relative to the moving sidewalk. How much time does it take the passenger to reach the opposite end of the walkway?
Problem 26. Assume it takes 8 minutes to fill a 35.0 gal gasoline tank. (1 U.S. gal = 231 cubic inches) (a) Calculate the rate at which the tank is filled in gallons per second. (b) Calculate the rate at which the tank is filled in cubic meters per second. (c) Determine the time interval, in hours, required to fill a same rate.
volume at the
Problem 27. A plane flies 955 km due east, then turns due north and flies another 469 km. Draw an x-y axis at the starting point with the positive x-axis pointing east, and determine the polar coordinates of the plane's finale position. Problem 28.
A car travels east at 89 km/h for 1 h. It then travels 26° east of north at 141 km/h for 1 h. (a) What is the average speed for the trip? (b) What is the average velocity for the trip? Problem 29. (a) If a particle's position is given by and x is in meters), what is it's velocity at t=1s?
(where t is in seconds,
(b) what is it's speed at t=1s? (c) Is there ever an instant when the velocity is 0? If so, give the time. Problem 30. The captain of a plane wishes to proceed due west. The cruising speed of the plane is 245 m/s relative to the air. A weather report indicates that a 38-m/s wind is blowing from the south to the north. In what direction, measured to due west, should the pilot head the plane relative to the air?
Problem 31. A missile is launched into the air at an initial velocity of 80 m/s. It is moving with constant velocity until it reaches 1000m, when the engine fails. (a) How long does it take it to reach 1000m? (b) How high does the missile go? (c) How long does it take for it to fall back to the earth? (d) How long does it stay in the air? (e) How fast is it going when it hits the ground? Problem 32. The highest barrier that a projectile can clear is 14 m, when the projectile is launched at an angle of 30.0 degrees above the horizontal. What is the projectile's launch speed? Problem 33. A rocket is fired vertically upwards with initial velocity 80 m/s at the ground level. Its engines then fire and it is accelerated at
until it reaches an
altitude of 1000 m. At that point the engines fail and the rocket goes into free-fall. Disregard air resistance. (a) How long was the rocket above the ground? (b) What is the maximum altitude? (c) What is the velocity just before it collides with the ground? Problem 34. An object is fired straight up at a speed of 9.8m/s. Compute its maximum altitude and the time it takes to reach that height. Ignore air resistance. Problem 35. A rock is dropped from rest into a well. (a) The sound of the splash is heard 4 s after the rock is released from rest. How far below to top of the well is the surface of the water? (the speed of sound in air at ambient temperature is 336m/s). (b) If the travel time for the sound is neglected, what % error is introduced when the depth of the well is calculated?
Problem 36. A ball is thrown upward with initial velocity v. What is the change in speed on the way up? What is the change in speed on the way down? Disregard air resistance. Problem 37. A displacement, s, of an object as a function of time, t, is given by a) Find an expression for the acceleration of the object b) Explain why this expression indicates that the acceleration is not constant Problem 38. Snow is falling vertically at a constant speed of 3 m/s. At what angle from the vertical do the snowflakes appear to be falling as viewed by the driver of a car traveling on a straight, level road with a speed of 60 km/h?
Problem 39. A dart is thrown horizontally with an initial speed of 10 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below P, 0.2 s later. What is the distance PQ? How far away from the dart board is the dart released? Problem 40. A boy walks to the store using the following path: 0.4 miles west, 0.2 miles north, 0.3 miles east. What is his total displacement? That is, what is the length and direction of the vector that points from her house directly to the store?
Problem 41. A motor scooter travels east at a speed of 13 m/s. The driver then reverses direction and heads west at 17 m/s. What was the change in velocity of the scooter? Problem 42. A bicycle travels 3.2 km due east in 0.1 h, the 3.2 km at 15.0 degrees east of north in 0.21 h, and finally another 3.2km due east in 0.1 h to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip? Problem 43. A swimmer dived off a cliff with a running horizontal leap. What must his minimum speed be just as he leaves the top of the cliff so that he will miss the ledge at the bottom which is 2 m wide and 9 m below the top of the cliff? Problem 44. A ferries wheel with radius 20 m which rotates counterclockwise, is just starting up. At a given moment, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00m/s and in gaining speed at a rate of
.
Find the magnitude of the passenger's acceleration at the instant.
Problem 45.
In an action film hero is supposed to throw a grenade from his car, which is going 90.km/h, to his enemy's car, which is going 110 km/h. The enemy's car is 15.8 m in front of the hero's when he lets go of the grenade. If the hero throws the grenade so its initial velocity relative to him is at an angle of 45(degree) above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. Ignore air resistance. Find the magnitude of the velocity both relative to the hero and relative to the earth.
Problem 46. A flowerpot falls from a windowsill 25.0 m above the sidewalk. (a) how fast is the flowerpot moving when it strikes the ground? (b) how much time does a passerby on the sidewalk below have to move out of the way before the flowerpot hits the ground?
Problem 47. A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s. (a) what will the ball\'s speed be when it returns to its starting point? (b) how long will the ball take to reach its starting point? Problem 48. Problem 4.14 of Serway & Jewett: A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle initial speed of the stream is
above the horizontal. If the
, at what height h does the water strike the building?
Problem 49. If it takes a player 3 seconds to run from the batter's box to the first base at an average speed of 6.5 m/s, what is the distance she covers in that time?
Problem 50. A car goes down a certain road at an average speed of 40 km/h and returns along the same road at an average speed of 60 km/h. Calculate the average speed for the round trip.
Problem 51. (Inquiry into Physics-5th ed.,Ostdiek,Bord) On a day the wind is blowing toward the south at 3m/s, a runner jogs west at 4m/s. What is the velocity of the air relative to the runner? Problem 52. (Inquiry into Physics-5th ed.,Ostdiek,Bord) A runner has an average speed of 4 m/s during a race. How far does the runner travel in 20 minutes? Problem 53. A car starts from the rest and accelerates uniformly for t=5 seconds over a distance of 100m. Find the acceleration of the car. Problem 54. On the moon, an object is dropped from a height of 2 m. The acceleration of gravity on the moon is to the surface of the moon.
. Determine the time it takes for the object to fall
Problem 55. A coin is dropped from a 400 m high tower. What is the coin's velocity when it hits the ground? How long does it take to get there?
Problem 56. Does the odometer of a car measure a scalar or a vector quantity? Problem 57. The speed of light is about
. Convert it into miles per hour (mph).
Problem 58. You are driving towards a traffic signal when it turns yellow. Your speed is 55 km/h, and your best deceleration has the magnitude of
. Your best
reaction time before breaking is . To avoid having the front of your car enter the intersection after the light turns red, should you break to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are (a) 40m and 2.8s, and (b) 32m and 1.8s? Problem 59. The tips of the blades in a food blender are moving with a speed of 20 m/s in a circle that has a radius of 0.06 m. How much time does it take for the blades to make one revolution? Problem 60. While you are traveling in a car on a straight road at 90 km/hr, another car passes you in the same direction; its speedometer reads 120km/hr. What is your velocity relative to the other driver? What is the other car's velocity relative to you?
Problem 61. A ball is thrown from a point 1 m above the ground. The initial velocity is 20 m/s at an angle of 40 degrees above the horizontal. (a) Find the maximum height of the ball above the ground. (b) Calculate the speed of the ball at the highest point in the trajectory. Problem 62. A tortoise can run with a speed of 10.0 cm/s, and a hare can run exactly 10 times as fast. In a race, they both start at the same time, but the hare stops to rest for 3.00 min. The tortoise wins by 10 cm. (a) How long does the race take? (b) What is the length of the race? Problem 63.
Emily takes a trip, driving with a constant velocity of 90 km/h to the north except for a 30 min rest stop. If Emily's average velocity is 75 km/h to the north, how long does the trip take?
Problem 64. To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 2000 m. If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event to qualify? Problem 65. A skier is accelerating down a 30 degree hill at
.
(a) What is the vertical component of her acceleration? (b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation is 300 m?
Problem 66. You are trying to cross a river that flows due south with a strong current. You start out in you motorboat on the west bank desiring to reach the east bank directly across from your starting point. Which direction should head your motorboat? Dram a picture of the river, the banks, and your motorboat, and include the relevant velocity vectors. What information would you need in order to determine the actual direction you need to head? Problem 67. (a) One liter ( ) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the (roughly circular) oil slick. Assume the oil molecules have a diameter of
.
(b) Recalculate for the Exxon Valdez oil spill (March 1989), in which 11 million gallons (42 million L) of crude oil coated Prince William Sound in Alaska. Problem 68.
The acceleration of an object as a function of time is Determine the
.
(a) velocity and (b) the position of the object as a function of time if it is located at x = 2 m and has a velocity of 3 m/s at time t = 0 s. Problem 69. An automobile traveling 90 km/h overtakes a 1.5-km-long train traveling in the same direction on a track parallel to the road. If the train's speed is 70 km/h, (a) how long does it take the car to pass it, and (b) how far will the car have traveled in the time?
Problem 70. Two cannonballs, A and B, are fired from the ground with identical initial speeds, but with launch angle of cannonball A larger than the launch angle of cannonball B. (a) Which cannonball reaches a higher elevation? (b) Which cannonball stays longer in the air? (c) Which cannonball travels farther? Problem 71. A stone falls freely from rest for 10 s. What is the stones displacement during this time. Problem 72. A typical atom has a diameter of
. What is this in inches?
Problem 73. A rock is shot up vertically upward from the edge of the top of the building. The rock reaches its maximum height 2 s after being shot. Them, after barely missing the edge of the building as it falls downward, the rock strikes the ground 8 s after it was launched. Find (a) upward velocity the rock was shot at; (b) the maximum height above the building the rock reaches; and
(c) how tall is the building? Disregard air resistance. Problem 74. A car going at 10 m/s undergoes an acceleration of far did it go when it was accelerating?
for 6 seconds. How
Problem 75. What is the displacement of a car accelerating from 5 m/s (right) to 10 m/s (right) in 2.0s?
Problem 76. A plane flies 50 degrees east of south for 100 km then 400 km north and then 20 degrees north of west for 250 km. Problem 77. Calculate the hang time of an athlete who jumps a vertical distance of .9 meters considering the acceleration of gravity is Problem 78. A man is driving at the speed 40 mph when he see an obstacle at distance 300 ft ahead of his position. The driver applies the brakes and decelerates at How long does it take him to stop the vehicle? How far from the obstacle will the driver be when he finally stops? Problem 79. The highest barrier that a projectile can clear is 20 m, when the projectile is launched at an angle of 40.0 degrees above the horizontal. What is the projectile's launch speed? Problem 80. You travel on the highway at a rate of 60 mph for 1 hour and at 50 mph for 2 hours and 40 mph for 3 hours. What is the total distance you have traveled? What is your average speed during the trip?
Problem 81. An object travels a distance of 5 km towards east, then 4 km towards north and finally 10 km towards east 1) what is total traveled distance? 2) what is resultant displacement?
Problem 82. Can two displacements (vectors) of different magnitudes be combined to give a zero displacement (resultant)? Problem 83. What is the speed (m/sec) needed for a stunt driver to launch from a 20 degree ramp to land 15 m away? What is his maximum height? Problem 84. A body moves 4 km towards East from a fixed point A and reaches point B. Then it covers 5 km towards North and arrives at point C. Find the distance and directions of the net displacement. Problem 85. A baseball player hits a homerun, and the ball lands in the left field seats, which is 120 m away from the point at which the ball was hit. The ball lands with a velocity of 20 m/s at an angle of 30 degrees below horizontal. Ignoring air resistance (A) find the initial velocity and the angle above horizontal with which the ball leaves the bat; (B) find the height of the ball relatively to the ground. Problem 86. A body covers 1/4 journey with a speed of 40 km/h, 1/2 of it with 50 km/h and remaining with the speed of 60 km/h. Calculate average speed for entire journey.
