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
 An object is dropped from a 56foot bridge over a bay. How long will it take for the object to reach the water?
 An object is dropped from the top of a 240foot tall observation tower. How long will it take for the object to reach the ground?
 A ball is dropped from a sixthfloor window at a height of 70 feet. When will the ball hit the ground?
 An object falls from the top of a 100foot 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.

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 object will reach the water in about 1.87 seconds.

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 object will reach the ground in about 3.87 seconds.

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 ball will hit the ground in about 2.09 seconds.

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 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
 A ball is dropped from a height of 50 feet. How long after it is dropped will it reach a height of 18 feet?
 A small object falls from a height of 200 feet. How long will it take to reach a height of 88 feet?
 A small object is dropped from a tenthfloor window (at a height of 110 feet). How long will it take for the object to pass the thirdfloor window (at a height of 35 feet)?
 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.

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

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

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

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 object will have fallen 100 feet 2.5 seconds after it is dropped.
Set 3: Determining How Long or at What Time an Object Will Reach a Specific Height
To review algebra problems involving geometric figures, go to The Height of a Falling Object Help
Practice
 An object on the ground is thrown upward at the rate of 25 feet per second. After how much time will the object hit the ground?
 A projectile is fired upward from the ground at the rate of 150 feet per second. How long will it take the projectile to fall back to the ground?
 An object is thrown upward from the top of a 50foot building. Its initial velocity is 20 feet per second. When will the object be 55 feet off the ground?
 A projectile is fired upward from the top of a 36foot building. Its initial velocity is 80 feet per second. When will it be 90 feet above the ground?
Solutions

In the formula h = –16 t ^{2} + v _{0} t + h _{0} , v _{0} = 25 and h _{0} = 0.
h = –16 t ^{2} + 25 t
We want to find t when h = 0.
The object will hit the ground after 1.5625 seconds.

In the formula h = –16 t ^{2} + v _{0} t + h _{0} , v _{0} = 150 and h _{0} = 0.
h = –16 t ^{2} + 150 t
We want to find t when h = 0.
The object will fall back to the ground after 9.375 seconds.

In the formula h = –16 t ^{2} + v _{0} t + h _{0} , v _{0} = 20 and h _{0} = 50.
h = –16 t ^{2} + 20t + 50
We want to find t when h = 55.
The object will reach a height of 55 feet at about 0.35 seconds (on its way up) and again at about 0.90 seconds (on its way down).

In the formula h = –16 t ^{2} + v _{0} t + h _{0} , v _{0} = 80 and h _{0} = 36.
h = –16 t ^{2} + 80 t + 36
We want to find t when h = 90.
The object will reach a height of 90 feet after about 0.80 seconds (on its way up) and again at about 4.20 seconds (on its way down).
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From Algebra Demystified: A SelfTeaching Guide. Copyright © 2003 by The McGrawHill Companies, Inc. All Rights Reserved.