Question

PLEASE HURRY

A ball is shot into the air using a brand new super-high-tech robotic arm to help baseball players practice catch fly balls.
The ball has an initial upward velocity of 64 feet per second. The height, h, of the ball after t seconds is given by the
equation: = -16t^2+ 64t+5
Approximately how long does it take for the ball to hit the ground. (Hint: That would be at a height of 0)
a about 4 seconds
b about 5 seconds
c about 3 seconds
d about 2 seconds

Answer 1

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