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Horizontal and Vertical Motion Problems

 

  1. A car traveling at 60 mi/hr applies its brakes and comes to rest in 0.8 sec.  Assuming the acceleration was constant during this time, calculate:
    1. The value of its acceleration in metric units.
    2. How far did the car travel while its brakes were applied?
  1. A body moving along a straight line has an initial velocity of +6.3 m/sec and maintains a steady acceleration of +0.25 m/sec2.
    1. What was its velocity after 3 sec?
    2. How far has it traveled during this time interval?
  1. A body moving along the x-axis passes the origin with a velocity of +3 cm/sec.  It then maintains a steady acceleration of +0.2 cm/sec2.  What is its final velocity when its x-coordinate is +40 cm?
  1. A body moving along the x-axis with a constant acceleration passes the origin with a velocity of  +5 cm/sec and 2 seconds later its x-coordinate is +6 cm.  Calculate the value of the body’s acceleration and specify its direction.
  1. A skater is gliding over the ice with a velocity of 2.6 m/sec.  Another skater pushes the first skater from behind and produces a steady acceleration of +1.3 m/sec2 until the first skater’s velocity attains 18.2 m/sec.
    1. How long did the push last?
    2. How far did the first skater travel during the push?
  1. An electron is emitted from a hot metal wire with an unknown velocity.  It then enters a device 4 cm in length which accelerates it at the rate of 3 x 1016 cm/sec2 in the same direction in which it is moving.  At the far end of this 4 cm device it enters another device which measures the electron’s velocity and determines it to be 7 x 108 cm/sec. What was its velocity when it was emitted from the hot wire?
  1. An automobile crashes into a tree at 60 mi/hr.  If this same car were to be dropped from above the ground so that is strikes the ground with the same velocity, from what height must it be dropped?
  1. When the automobile is problem #7 crashed into the tree at 60 mi/hr, its front end was brought to rest in a very short distance, but the body buckled and the driver traveled a further distance of 1 ft.  Assuming that his acceleration was constant:
    1. Calculate its value.
    2. Compare the velocity of this acceleration to that of gravity.
  1. An engine traveling along a straight track passes a station with a velocity of 15 cm/sec.  It then maintains a steady forward acceleration of 0.02 m/sec2 and reaches the next station 10 minutes later.
    1. What is the distance between the two stations?
    2. What was its final velocity at the next station?
  1. An automobile starts from rest and reaches a velocity of 60 mi/hr in 10 seconds.
    1. What was its acceleration?
    2. How far did it travel?
  1. A man throws a ball vertically into the air with a vertical velocity of 96 ft/sec.  Two seconds later he throws another ball vertically upward with the same velocity.  At what height above the ground will the two balls pass?
  1. A workman accidentally drops his hammer while working on a high building.  If it takes 8 seconds for the hammer to reach the ground:
    1. How high was the building?
    2. With what velocity does it strike the ground?
  1. In diving from a high platform, a swimmer is moving downward with a velocity of 48 ft/sec when she enters the water.
    1. From what height did she fall?
    2. How long did it take her to reach the water?
  1. A golf ball has a velocity of “V” when it was dropped from a height “H”.  If it had a velocity of  “2V”, from what height would it have fallen?
  1. A lead brick takes 2 seconds to fall to the ground.  A gold brick takes 3 seconds to fall to the ground.  What is the difference in height from which the two bricks were dropped?
  1. A bomb is dropped from an airplane which is flying at 4,000 ft when it is directly over the target.  If the plane is flying horizontally at 300 mi/hr, how far will the bomb miss the target?
  1. A mail plane in straight and level flight, moving at 100 mi/hr at 1,500 ft above the ground, releases some mailbags to be picked up on the ground.
    1. How long do the bags take to reach the ground?
    2. With what velocity do they strike the ground?
  1. A body falls for a period of 10 seconds before hitting the ground.
    1.  How far did it take to fall?
    2. With what velocity did it strike the ground?
  1. A car starting from rest attains a velocity of 35 mi/hr in 7 seconds.  What was the car’s acceleration?
  1. An automobile moving at 60 mi/hr comes to rest 30 seconds after the brakes are applied.  What is its acceleration?
  1. How long will it take an object to fall to the ground from the top of the Empire State building, which is approximately 1.024 ft tall?
  1. A ball rolling down a hill is being accelerated at the rate of 4 ft/sec2.
    1. What will be its final velocity after it has traveled 72 ft?
    2. How long does it take to travel 72 ft?
  1. A train traveling at 50 mi/hr is brought to rest in 5 minutes.
    1. What was its acceleration?
    2. How far does it travel in coming to rest?
  1. A stone dropped from the top of a building hits the ground in 4.5 seconds.
    1. How high is the building?
    2. What is the velocity of the stone as it strikes the ground?
  1. A bullet fired vertically upward, leaves the muzzle of the gun with a velocity of 320 ft/sec.
    1. How high will the bullet rise?
    2. How long will it be in the air?
  1. A sled starting from rest runs 250 ft down a hill in 10 seconds.
    1. What is its acceleration?
    2. What is its final velocity at the bottom of the hill?
  1. An automobile traveling at 45 mi/hr slow at the rate of 3 mi/hr/sec.  How long will it take to stop?
  1.  A cannon ball is fired vertically into the air with a velocity of 900 m/sec. 
    1. How high has it gone after 10 seconds?
    2. What is its velocity at that point?
  1. A man stands at the edge of a 59 m high cliff.  He throws a ball vertically upward with a velocity of 16 m/sec. 
    1. What is the ball’s TOTAL time in the air?
    2. What is the ball’s TOTAL distance that it travels (up and down)?
    3. What is the velocity with which the ball strikes the ground at the base of the cliff?
  1. Superman is standing at a window 200 ft above a lake when a man that fell out of a window 80 ft above superman’s location passes Superman’s window.
    1. How long will it take the man to reach the water below?
    2. What must be Superman’s acceleration if he is to catch the man a split second before the man hits the water?
  1. A rocket is capable of providing 9 g’s of acceleration.  What is its final velocity if this is achieved in 30 meters?
  1. A boy throws a stone from the ground to the top of a flagpole.  The stone returns to the ground in 6 seconds.
    1. How high is the flagpole?
    2. With what velocity must the stone be thrown?
  1. If a ball is dropped and attains a velocity of 29.31 m/sec in 0.08 seconds.
    1. What is the acceleration of gravity at this location?
    2. How far has the ball traveled?
  1. An automobile is accelerated from 45 mi/hr to 65 mi/hr in 8 seconds.
    1. What is its acceleration?
    2. How far did it travel?
  1. An arrow is projected vertically upward from the top of a 550 m high building with a velocity of 88 m/sec.  Assuming that it just misses the edge of the building on the way down.
    1. How far above the building does it rise?
    2. With what velocity does it strike the ground?
    3. How long was it in the air?
  1. A baby falls out of a window 40 ft above the window where Superman is standing.  Superman’s window is 80 ft above the ground and he must catch the baby 4 ft above the ground.
    1. What must Superman’s acceleration be to catch the baby?
    2. What is Superman’s velocity as he catches the baby?
    3. What must Superman’s acceleration be as he slows down and stops after catching the baby?
  1. Superman is standing on a window ledge 45 m above the sidewalk.  A man falls out of a window 8 m below Superman’s location.
    1. What must Superman’s acceleration be in order to catch the man just before the man hits the sidewalk?
    2. What would be Superman’s final velocity just as he catches the man?
    3. What is the man’s velocity just as Superman catches him?
  1. The velocity of a train is uniformly reduced from 35 m/sec to 15 m/sec while traveling a distance of 500 m.
    1. What is the train’s acceleration?
    2. How much farther will the train travel before coming to rest, assuming it maintains this acceleration?
  1. A stone is thrown vertically downward with an initial velocity of 8 m/sec from a height of 800 meters.
    1. Find the time it takes to strike the ground.
    2. What is the final velocity of the stone as it strikes the ground?
    3. How far above the ground will the stone be after 3.5 seconds of travel?
  1. A stone is projected vertically upward with a velocity of 80 m/sec from the top of a tower 2240 meters in height.
    1. What maximum height does the stone attain above the base of the tower?
    2. With what velocity does it strike the ground at the base of the tower?

  1. A rocket launches a satellite into orbit.  The rocket attains a velocity of 2.9 x 104 km/hr in 2.05 minutes.  The rocket has enough fuel to maintain a constant acceleration for one hour. 
    1. What is the rocket’s acceleration in m/sec2 for the first 2.05 minutes?
    2. What is the rocket’s velocity after accelerating for one hour?
    3. What distance will the rocket travel during the hour?
  1. A stone is dropped from a balloon which is ascending at the rate of 5 m/sec when the balloon is 353 m above the ground.
    1. How long will it take the stone to reach the ground?
    2. With what velocity will the stone strike the ground?
  1. An object with an initial velocity of 20 m/sec is accelerated at 8 m/sec2 for 5 minutes.
    1. What is its total displacement?
    2. What is its final velocity?
  1. At a July 4th celebration a solid propellant rocket is accelerated vertically upward until it reaches a velocity of 60 m/sec at a height of 100 m.  At this point, the propellant is exhausted and the acceleration ceases.
    1. How much time does it take the rocket to return to a velocity of 60 m/sec?
    2. Once the propellant is exhausted, how long will it take the rocket to return to the ground?

  45.  Wiley Coyote is standing on a ledge of a mountain side below Road Runner's position.  Wiley throws a stick of dynamite upward, which travels 50 ft, but returns toward Wiley and continues to fall passed Wiley to explode at the base of the mountain far below.  If the dynamite's total time in the air is 8.84 seconds, with what speed did Wiley throw the dynamite?  What is Wiley's elevation above the base of the mountain?

 

Multiple Choice Self-Test:

  1. Speed is the magnitude of:
    1. Acceleration
    2. Final velocity
    3. Average acceleration
    4. Velocity and is therefore scalar
  1. Instantaneous velocity is:
    1. Symbolized as “V”
    2. Impossible
    3. Velocity passing a given point
    4. Average velocity between two point
  1. Acceleration is symbolized by:
    1. L/t
    2. T2/L
    3. L/t2
    4. T/l
  1. The distance moved in constant acceleration starting from rest is proportional to:
    1. The square of the velocity.
    2. The square root of the reciprocal of the time interval.
    3. The square of the tine interval.
    4. The time interval.
  1. Which of the following equations is correct?
    1. Vf2  =  Vo2  +  2 a t
    2. Vf2  =  Vo2  + 2 a S
    3. Vf2  =  Vo2  -  2 a S
    4. Vf  =  2 a S
  1. A feely falling object near the Earth’s surface undergoes:
    1. Constant acceleration
    2. Changing acceleration
    3. Constant velocity
    4. Air resistance
  1. Acceleration due to gravity is:
    1. 9.8 m/sec
    2. 98 m/sec2
    3. 32 ft/ft3
    4. 32 ft/sec2
  1. The gravitational attraction on objects is greatest at:
    1. The equator
    2. The North Pole
    3. New York
    4. Clarks Summit
  1. Terminal velocity is:
    1. Velocity is zero
    2. Acceleration is zero
    3. Original velocity
    4. Average velocity
  1. Acceleration is what type of quantity:
    1. Vector
    2. Scalar
  1. When an object undergoes uniform acceleration, its displacement equals the sum of this initial velocity times the elapsed time plus:
    1. 2 times the acceleration.
    2. 1/3rd times the acceleration.
    3. ½ times the acceleration times elapsed time squared.
    4. 3 times the acceleration times the elapsed time squared.
  1. Which of the following is not an opposing obstacle for a freely falling object:
    1. Air resistance
    2. Gravity
    3. Wind
    4. Moisture in air causing greater density
  1. The time rate of change of velocity is:
    1. Momentum
    2. Speed
    3. Inertia
    4. Acceleration
  1. The relationship between acceleration and force is given by Newton’s:
    1. First Law
    2. First and Third Law
    3. Second Law
    4. Third Law
  2. Newton’s First Law of Motion is usually called the law of:
    1. Simple harmonic motion
    2. Action-reaction
    3. Universal gravitation
    4. Inertia
  1. An object has acceleration because:
    1. It is free to move
    2. Forces act on it
    3. Its speed is constant
    4. An unbalanced force act on it
  1. For every action there is an equal and opposite reaction is a statement of Newton’s:
    1. First Law
    2. Second Law
    3. Third Law
    4. Law of Universal Gravitation
  1. According to Newton’s First Law:
    1. All falling objects move at the same speed.
    2. Motion at a constant speed in a straight line requires no force to explain the motion.
    3. An object can only remain stationary if a force acts on it.
    4. Any moving body must have a force acting on it.
  1. Which of the following situations is most closely connected to Newton’s Second Law of Motion:
    1. A tug-of-war between two exactly balanced forces.
    2. An object moving in a straight line at a constant speed.
    3. A rock held by a string.
    4. Freely falling bodies moving at the same speed.
  1. A body undergoing a uniform motion of  3.5 km/hr/sec:

a.      Increases its speed by 3.5 km/hr each second of travel.

b.      Travels 3.5 km farther each second of travel.

c.      Maintains an unchanging speed of 3.5 km/hr each second of travel.

d.      Is impossible for the unit given.

 

  1. A negative acceleration means that the body:

a.      Is maintaining an unchanging velocity.

b.      Is falling toward Earth from an elevation.

c.      Is reducing its velocity over time.

d.      Is moving in reverse.

 

Go to Sample 1 for a demonstration on solving "relationship" problems, such as #22 and 23 below.

  1. Two trains, “A” and “B”, moving with the same velocity are brought to rest.  Train “A” travels 10 times the distance of train “B”.  What is the relationship between the acceleration of  “A” with respect to “B”?

a.      aA =  0.1 aB

b.      aA = 3.16 aB

c.      aA = 10 aB

d.      aA = 100aB

 

  1. Object “A” and object “B” are dropped simultaneously from two different airplanes at different altitudes.  If object “A” strikes the ground with a velocity that is one-fourth the velocity of object “B”, what is the relationship between their two heights?

a.      SA = 0.0625 SB

b.      SA = 0.125 SB

c.      SA = 0.250 SB

d.      SA = 0.500 SB

 

  1. A superwoman falls 44 meters from the 17th floor of a building and lands on a metal ventilator box, which she crushes to a depth of 46 cm before coming to rest.  She only suffers minor scratches.  Neglecting air resistance, calculate superwoman’s acceleration while she is in contact with the box.

a.      – 9.38

b.      – 9.70

c.      – 31.52

d.      – 937.61