Question

use this form h(t) = -a (t-10)^2+100a to find the time after being fired out the cannon that the ball obtain maximum height. the maximum height of the cannon ball is 20m (above the end of the barrel which is 4.2 m high)

Answer 1

What's the problem? If you find h'(t) , at max height h'(t) is zero

Answer 2

which height must you use to get the time when the ball has reached the max height

Answer 3

Use 20m

Answer 4

20=-a(t-10)^2 +100a is it correct the first step?

Answer 5

or is it 20t

Answer 6

Differentiate it first, because
h'(t) is velocity, at max height, velocity is zero

Answer 7

answer is 20s?

Answer 8

Nope,
\[h(t)=-a(t-10)^2+100a \\ \\ h'(t)=-2a(t-10)=0 \\ \\ t=10s\]

Answer 9

why -2a?

Answer 10

You're differentiating -a(t-10)^2, using power rule

Answer 11

ok thanks a lot for all the trouble

Answer 12

Ok so you got the answer?

Answer 13

yes thanks 10?

Answer 14

yes