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?
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.