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# The Height of a Falling Object Practice Problems (page 2)

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

### 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

1. 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?
2. 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?
3. An object is thrown upward from the top of a 50-foot building. Its initial velocity is 20 feet per second. When will the object be 55 feet off the ground?
4. A projectile is fired upward from the top of a 36-foot building. Its initial velocity is 80 feet per second. When will it be 90 feet above the ground?

#### Solutions

1. 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.

2. 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.

3. 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).

4. 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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