Question

This Question: 1 pt

A baseball is hit so that its height in feet after t seconds is s(t) = - 4t"" + 20t+2.
(a) How high is the baseball after 1 second?
(b) Find the maximum height of the baseball.​

Answer 1

Answer with Step-by-step explanation:

We are given that

Height of ball after t seconds is given by

`s(t)=-4t^2+20t+2`

a.Substitute the value of t=1

`s(1)=-4(1)+20(1)+2=-4+20+2=18 ft`

b.Differentiate w.r.t x

`s'(t)=-8t+20`

`s'(t)=0`

`-8t+20=0`

`8t=20`

`t=(20)/(8)=2.5`

Again differentiate w.r.t t

`s''(t)=-8<0`

Hence, the height is maximum at t=2.5 s

`s(2.5)=-4(2.5)^2+20(2.5)+2=27`

Maximum height of the baseball=27 ft