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.

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