Question

1. A cannonball is fired and its height, h, in meters above the

ground, t seconds after being fired is given by
h (t)= -5t² + 40t + 3. Determine how many seconds it takes
to reach its maximum height.

Answer 1

Explanation:

any extreme point (incl. the requested max.) is a zero of the first derivation of the function.

h'(t) = -10t + 40

and that must be 0.

so,

0 = -10t + 40

10t = 40

t = 40/10 = 4

it takes 4 seconds to reach the max. height.

and that max. height is

-5×4² + 40×4 + 3 = -80 + 160 + 3 = 83 m.