408 algebra De mystif ieD
when h = 0, so h 0 = −16t^2 + 1600 becomes 0 = −16t^2 + 1600. We solve this
for t.
016 1600
16 1600
100
100
10 10
2
2
2
=− +
=
=
=±
==−
t
t
t
t
tt(isnotasolution)
The object will hit the ground 10 seconds after it is dropped.
A ball is dropped from the top of a four-story building. The building is
48 feet tall. How long will it take for the ball to reach the ground?
Because the object is dropped, the initial velocity, v 0 , is zero: v 0 = 0.
The object is dropped from a height of 48 feet, so h 0 = 48. The formula
h = − 16 t^2 + v 0 t + h 0 becomes h = − 16 t^2 + 48. The object hits the ground
when h = 0.
ht
t
t
t
tt
=− +
=− +
=
=
==−
16 48
01648
16 48
3
33
2
2
2
2
(isnotaasolution)
t≈ 17 3.
The ball will reach the ground in about 1.73 seconds.
PRACTICE
- An object is dropped from over a bay. If the ball is dropped 56 feet
above the surface of the water, how long will it take for the object to
reach the water? - 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? - A ball is dropped from a sixth floor window at a height 70 feet. When
will the ball hit the ground? - An object falls from the top of a 100-foot communications tower. How
long will it take for the object to hit the ground?
PRACTICE
- An object is dropped from over a bay. If the ball is dropped 56 feet
above the surface of the water, how long will it take for the object to
PRACTICE
- An object is dropped from over a bay. If the ball is dropped 56 feet