Question

A dolphin jumps out of the water with

an initial velocity of 20 feet per second.
The dolphin's height, h, after t seconds
of time can be modeled by the
equation:
h(t) = -16t2 + 20t.
Determine how long it took for the
dolphin to return to the water.

Answer 1

`t=1.25\ sec`

Explanation:

we have

`h(t)=-16t^(2)+20t`

where

t is the time in seconds

h is the dolphin's height in feet

we know that

When the dolphin return to the water the value of h(t) is equal to zero

so

For h(t)=0

`0=-16t^(2)+20t`

`16t^(2)=20t`

Simplify

`16t=20`

`t=(20)/(16)`

`t=(5)/(4)=1.25\ sec`

see the attached figure to better understand the problem