Example
An object is dropped from the roof of a
60-foot building. How longbmust it fall to reach a height of 28 feet?
In the formula h = –16t2 + v0t + h0, h0 is 60 and v0 is zero (because the object is dropped). The object reaches a height of 28 feet when h = 28.
The object will reach a height of 28 feet
after about 1.41 seconds.
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 ¼ 20 feet.)
Solutions
Negative values of t will not be solutions.
1. In the
formula h = –16t2 + v0t
+ h0, h0 = 50 and v0 = 0.
h = –16t2 + 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.
2. In the
formula h = –16t2 + v0t
+ h0, h0 = 200 and v0 = 0.
h = –16t2 + 200
We want to find t when h = 88. ¼ 0.
The object will reach a height of 88 feet
after about 2.65 seconds.
3. In the
formula h = –16t2 + v0t
+ h0, h0 = 110 and v0 = 0.
h = –16t2 + 110
We want to find t when h = 35.
The object will pass the third floor window
after about 2.17 seconds
4. In the
formula h = –16t2 + v0t
+ h0, h0 = 120 and v0 = 0. h = -16t2
+ 120 The object has fallen 100 feet when the height is 120 – 100 = 20 feet, so we want to find t when h ¼
20.
The object will have fallen 100 feet 2.5
seconds after it is dropped.
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