Question

A firecracker is fired straight up into the air out of a

window of a building. Its height, in feet, is given by
16t² + 192t + 160, where t is the time, in
seconds, the fircracker has been in the air.
h
-
At some point in its path it reaches a highest point.
the greatest height is
Select an answer and the firecracker reaches it after
I
Select an answer

Answer 1

The greatest height is 736 ft and the firecracker reaches it after 6 seconds.

f(t)= -
`16t^(2)`+192t+160

f'(t)= -32t+192.

At maximum height, f'(t)= 0

-32t+192 = 0

t=192
`(192)/(32)` = 6

Greatest height = h(6)= -
`16.6^(2)`+192(6)+160

=-576+1152+160 = 736 ft

Question:

A firecracker is fired straight up into the air out of a window of a building. Its height, in feet, is given by -16t² + 192t + 160, where t is the time, in seconds, the fircracker has been in the air. At some point in its path it reaches a highest point. Find the highest point and the time at which it reaches that pint.