Question

How long antermg5. Mitch throws a ball over a 20-foot fence to a baseball field. The height, h(1), of the ball at time iseconds after it was thrown can be modeled by the equation h(t)=-161 +301 +6. Which statement(s)is/are true? Then explain why the others are false?

Answer 1

Answer:

Option D is correct

Explanations:

The model equation for the height of the ball at time t is given as:

h(t) = - 16t² + 30t + 6

Note:

The ball reaches a maximum height at a time when dh/dt = 0

The height of the ball at any time t is given by h(t) = - 16t² + 30t + 6

From h(t), dh/dt will be calculated as:

dh/dt = -32t + 30

At maximum height, dh/dt = 0

0 = -32t + 30

32t = 30

t = 30/32

t = 0.94 s

Therefore, the ball reaches the maximum height at 0.94 second

Let us find the position of the ball at t = 2 seconds

h(t) = - 16t² + 30t + 6

h(2) = -16(2)² + 30(2) + 6

h(2) = -64 + 60 + 6

h(2) = 2

At t = 2 seconds, the height of the ball is 2 feet

Let us find the position of the ball at t = 1.5 seconds

h(t) = - 16t² + 30t + 6

h(1.5) = -16(1.5)² + 30(1.5) + 6

h(1.5) = -36 + 45 + 6

h(1.5) = 15

At 1.5 seconds, the ball is 15 feet high

Since the height of the ball, h(t) is a function of time, the ball can clear the fence depending on the time, t, spent in the air