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The Height of a Falling Object Practice Problems

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By — McGraw-Hill Professional
Updated on Sep 27, 2011

The Height of a Falling Object Practice Problems

Set 1: Determining When an Object Will Reach the Ground

To review algebra problems involving geometric figures, go to The Height of a Falling Object Help

Practice

  1. An object is dropped from a 56-foot bridge over a bay. How long will it take for the object to reach the water?
  2. An object is dropped from the top of a 240-foot tall observation tower. How long will it take for the object to reach the ground?
  3. A ball is dropped from a sixth-floor window at a height of 70 feet. When will the ball hit the ground?
  4. An object falls from the top of a 100-foot communications tower. After how much time will the object hit the ground?

Solutions

For all of these problems, both a negative t and a positive t will be solutions for the quadratic equations. Only the positive t will be a solution to the problem.

  1. For the formula h = –16 t 2 + v 0 t + h 0 , h 0 = 56 and v 0 = 0 (because the object is being dropped). The object reaches the ground when h = 0.

    The Height of a Falling Object Solutions

    The object will reach the water in about 1.87 seconds.

  2. For the formula h = –16 t 2 + v 0 t + h 0 , h 0 = 240 and v 0 = 0 (because the object is being dropped). The object reaches the ground when h = 0.

    The Height of a Falling Object Solutions

    The object will reach the ground in about 3.87 seconds.

  3. For the formula h = –16 t 2 + v 0 t + h 0 , h 0 = 70 and v 0 = 0 (because the object is being dropped). The object reaches the ground when h = 0.

    The Height of a Falling Object Solutions

    The ball will hit the ground in about 2.09 seconds.

  4. For the formula h = –16 t 2 + v 0 t + h 0 , h 0 = 100 and v 0 = 0 (because the object is being dropped). The object reaches the ground when h = 0.

    The Height of a Falling Object Solutions

    The object will hit the ground after 2.5 seconds.

Set 2: Determining When an Object Will Reach a Specific Height

To review algebra problems involving geometric figures, go to The Height of a Falling Object Help

Practice

  1. A ball is dropped from a height of 50 feet. How long after it is dropped will it reach a height of 18 feet?
  2. A small object falls from a height of 200 feet. How long will it take to reach a height of 88 feet?
  3. A small object is dropped from a tenth-floor window (at a height of 110 feet). How long will it take for the object to pass the third-floor window (at a height of 35 feet)?
  4. An object is dropped from 120 feet. How long will it take for the object to fall 100 feet? ( Hint : the height the object has reached after it has fallen 100 feet is 120 – 100 = 20 feet.)

Solutions

Negative values of t will not be solutions.

  1. In the formula h = –16 t 2 + v 0 t + h 0 , h 0 = 50 and v 0 = 0. h = –16 t 2 + 50

    We want to find t when h = 18.

    The Height of a Falling Object Solutions

    The ball reaches a height of 18 feet about 1.41 seconds after it is dropped.

  2. In the formula h = –16 t 2 + v 0 t + h 0 , h 0 = 200 and v 0 = 0. h = –16 t 2 + 200

    We want to find t when h = 88.

    The Height of a Falling Object Solutions

    The object will reach a height of 88 feet after about 2.65 seconds.

  3. In the formula h = –16 t 2 + v 0 t + h 0 , h 0 = 110 and v 0 = 0. h = –16 t 2 + 110

    We want to find t when h = 35.

    The Height of a Falling Object Solutions

    The object will pass the third floor window after about 2.17 seconds.

  4. In the formula h = –16 t 2 + v 0 t + h 0 , h 0 = 120 and v 0 = 0. h = –16 t 2 + 120

    The object has fallen 100 feet when the height is 120 – 100 = 20 feet, so we want to find t when h = 20.

    The Height of a Falling Object Solutions

    The object will have fallen 100 feet 2.5 seconds after it is dropped.

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