Claire kicks a football. It’s height in feet is given by h(t)=-16t^2 + 48t where t represents the time in seconds after kick. How many seconds have gone by when the football is at its highest point?

Answer 1

The problem can be solved using calculus.

We want to obtain the maximum of the function h = h(t).

First, we derive h with respect to t,

dh/dt = - 2(16)t + 48 = 48 - 32t

We then equate to zero and solve for t,

48 - 32t = 0

t = 48/32 = 1.5

So, the maximum altitude for the ball is acquire at t = 1.5 seconds.

And the height is,

h = 48(1.5) - 16(1.5) * 2 = 36 ft