Question

A tennis ball bounces so that its initial speed straight upwards is b feet per second. Its height s in feet at time t seconds is given by s = bt − 16t2
a) Find the velocity v = ds/dt at time t.
b) Find the time at which the height of the ball is at its maximum height.
c) Find the maximum height.

Answer 1

found a I just differentiate leaving
b-32t
let v(0)
0=b-32t
t=b/32

finding the max height
s(b/32) when velocity is 0
but they answer that---s( b/32)=b^2/64

why would they put b to a raised power. like they did in the answer.

Answer 2

need help?

Answer 3

s(b/32) = b(b/32) − 16(b/32)^2
= b^2 / 32 - 16 *b^2 / 1024
= 32b^2 / 1024 - 16b^2 / 1024
= 16b^2 / 1024 = b^2 / 64

Answer 4

ty I plgged it in but received a different answer.
I made a mistake somewhere.

ty again