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 equations h(t) = -16t^2 + 39t. If the bell is 25 ft above the ground, will it be hit by the ball? Why or why not?

A.Yes
B) No

Answer 1

The ball will hit the bell. The height of the ball can be modeled by the equation h(t) = -16t^2 + 39t. By setting the height of the ball equal to the height of the bell and solving for time, we find that the ball will hit the bell at t = 0.625 and t = 1.563.

Step-by-step explanation:

The height of the ball can be modeled by the equation h(t) = -16t^2 + 39t, where h(t) represents the height at time t. In this equation, t represents time in seconds and h(t) represents height in feet. To determine if the ball will hit the bell, we need to find the time when the height of the ball is equal to the height of the bell. We can set h(t) equal to 25 and solve for t:

-16t^2 + 39t = 25

By rearranging the equation and solving for t, we get:

16t^2 - 39t + 25 = 0

Using the quadratic formula, we find that the roots of this equation are t = 0.625 and t = 1.563. Since both roots are positive and within the time range of the ball's flight, the ball will hit the bell.