Question

Please help!! 45 points!!

A ball is projected into the air. Its height at time, t, is given by the equation h=-16t^2 + 100t + 2. When will the ball return to the ground?

A.0.02 sec
B. 6.3 sec
C. 6.5 sec
D. 16 sec

Answer 1

The ball will return to the ground at t = 16 seconds, so the correct answer is D.

Explanation:

To find when the ball will return to the ground, we need to find the time at which the ball's height is equal to 0. We can do this by setting the height equation equal to 0 and solving for t.h = -16t^2 + 100t + 2

0 = -16t^2 + 100t + 2

-2 = -16t^2 + 100t

-0.125t = -2

t = 16

Answer 2

B. 6.3 sec

Explanation:

To find the time when the ball will return to the ground, we need to find the value of t when h is equal to 0 (since height = 0 means the ball is on the ground). We can do this by substituting 0 for h in the given equation and solving for t.

So, let's start by substituting 0 for h:

h = -16t^2 + 100t + 2

0 = -16t^2 + 100t + 2

-16t^2 + 100t + 2 = 0

This is a quadratic equation, which we can solve using the quadratic formula:

t = (-100 +/- sqrt(100^2 - 4(-16)(2)) ) / (-2(-16))

t = (-100 +/- sqrt(10000 + 128)) / 32

t = (-100 +/- sqrt(10128)) / 32

t = (-100 +/- 100.64) / 32

t = (200.64) / 32

t = 6.3125

Since the ball is projected into the air and then falls back down to the ground, the time when it returns to the ground must be a positive value. Therefore, the solution to the problem is t = 6.3 sec