Question

A ball is shot from a cannon into the air. The equation that's gives the height (h) of the ball of any time (t) is: h(t)= -16t^2 + 40t + 1.5

Answer 1

26.5 units

Explanation:

The height of the ball at any time t is given by :

`h(t)= -16t^2 + 40t + 1.5` ...(1)

We need to find the maximum height of the ball.

For maximum height, put
`(dh)/(dt)=0`

i.e.

`(d( -16t^2 + 40t + 1.5))/(dt)=0\\\\-32t+40=0\\\\t=(40)/(32)\\\\t=1.25\ s`

Put t = 1.25 in equation (1) to find the maximum height.

So,

`h(t)= -16(1.25)^2 + 40(1.25) + 1.5\\\\=26.5\ units`

So, the maximum height reached by the ball is 26.5 units.