math 117 problem

Question

A ball projected upwards with a velocity on 128 feet per minute from a height of 5 feet above the ground is modelled by the function h(t)= -16t^2+128t+5

a. when will the ball reach its maximum height?

b. determine the maximum height that the ball reached.

c. find the x-intercept and explain its meaning in the context of the problem.

d. after how many seconds will the ball be 100 feet above the ground?

e. find the y-intercept and explain its meaning in the context of the problem.

Answer 1

Answer 2

Hi Amanda,

I'm assuming that you are allowed to use a graphing calculator for this problem.

If you enter the function into your calculator, you will see the graph has a global maximum at (4,261). The point (4,261) means at 4minute, the ball will reach its maximum height at 261 feet.

A: 4

B: 261

C: The x-intercept is at (8.039,0), meaning at 8.039 minutes, the ball will fall to the ground.

D: For this question, we are looking for the value of t for the equation of 100=-16t^2+128t+5. Using a graphing calculator, we see that at .828 minutes, the ball was 100 feet above the ground. Converting minutes to seconds, the answer should be 49.68 sec.

E: To find the y-intercept, we need to plug 0 in for all t. The answer is h(t)=5, which means at 0 minutes, the ball had an initial altitude of 5 ft.