Question

A cannonball is fired into the air. It's height, h, in metres after t seconds is given by the relation:

h=-4.6 (t-7.5)^2+285

a) what is the maximum height reached by the cannon and what time is this reached.
b) what was the initial height of the cannon?
c) what is the height of the cannon after 10.5 seconds?
d) how long is the cannon in the air?

Answer 1

Please answer with the steps

Answer 2

a) max height is when f'(t)=0 {solve this for t, critical point}
i get t=7.6 seconds
so max height = h(7.6)

b)Initial height is height at t=0. so initial height is h(0) = 26.35feet
c) height after 10 seconds = h(10)
d)\[\href{ http://www.wolframalpha.com/input/?i=roots+-4.6+%28t-7.5%29%5E2%2B285+ }{Total time}\]

Take positive time