Answer:
To determine how long it takes for the ball to hit the ground, we need to find the value of t when the height, h, is equal to 0.
The given equation for the height of the ball, h, is:
h = -16t^2 + 64t + 5
Setting h to 0 and solving for t, we get:
0 = -16t^2 + 64t + 5
Using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -16, b = 64, and c = 5, we get:
t = (-64 ± sqrt(64^2 - 4(-16)(5))) / 2(-16)
t = (-64 ± sqrt(4096 + 320)) / (-32)
t = (-64 ± sqrt(4416)) / (-32)
Taking the positive root since the negative root is not applicable in this context, we get:
t = (-64 + 66.38) / (-32)
t = -2.38 / (-32)
t ≈ 0.0746 seconds
Therefore, it takes approximately 0.0746 seconds for the ball to hit the ground.
Answer: d about 2 seconds