Question

One of the games at a carnival involves trying to ring a bell with a ball by hitting a lever that propels the ball into the air. The height of the ball is modeled by the equation h(t)= -16t^2+39t. if the bell is 25ft above the ground, will it be hit by the ball?

Answer 1

Answer:

Ball will not hit bell.

Explanation:

The height of the ball is modeled by the equation h(t)= -16t²+39t

We need to find if the bell is 25 ft above the ground, will it be hit by the ball.

So we need to find maximum height of the ball.

For maximum height we have

                   $\frac{dh}{dt}=0\\\\\frac{d}{dt}\left ( -16t^2+39t\right )=0\\\\-32t+39=0\\\\t=1.22s$

Substituting in h(t) = -16t²+39t

Maximum height reached = h(1.22) = -16 x 1.22²+39 x 1.22 = 23.77 ft

So maximum height reached is less than height of bell.

Ball will not hit bell.