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
.

If the bell is 25 ft above ground will it be hit by the ball?


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 25 ft above ground will it be hit by the ball?

Answer 1

We need to find the time (t) at which the height of the ball is equal to 25 ft.

So, we set h(t) = 25 and solve for t:
-16t^2 + 39t = 25
-16t^2 + 39t - 25 = 0

To solve this quadratic equation, we can use the quadratic formula:
t = (-39 ± sqrt(39^2 - 4(-16)(-25))) / 2(-16)
t = (-39 ± sqrt(1521 - 1600)) / -32
t = (-39 ± sqrt(921)) / -32

Therefore, t = (-39 + 30.35) / -32 or t = (-39 - 30.35) / -32
This gives us t = -0.27 or t = 1.52

Since time cannot be negative, we discard -0.27 and consider t = 1.52.

Therefore, the ball will hit the bell when t = 1.52 seconds.