Question

Raylin went to the park with her friends and found a soccer ball. She picked up the soccer ball and kicked it as high as she could. The path of the ball can be represented by h= -16t2 +27t+3
What is the maximum height of the soccer ball? _______________________

How long will it take the ball to reach the ground?

Answer 1

Answer:

The maximum height is: $h(t_{max})=14.39 \: u$  

The ball reaches the ground in 1.79 s.

Step-by-step explanation:

We need to take the derivative and equal to zero to find the time at the maximum height.

$h(t)=-16t^{2} +27t+3$ (1)

$\frac{dh(t)}{dt}=-32t +27=0$

$t_{max} =\frac{27}{32}$

$t_{max} =0.84\: u$

Now, we just need to put t(max) into equation (1) to find h(max)

$h(t_{max})=-16(0.84)^{2} +27(0.84)+3$

$h(t_{max})=-16(0.84)^{2} +27(0.84)+3$

$h(t_{max})=14.39 \u$  

If we want to get the time when the ball reaches the ground we just need to equal h(t) to zero.

$0=-16t^{2} +27t+3$

Let's solve this quadratic equation.

We will get two solutions and we must choose the positive value.

t1 = 1.79 u

t2 = -0.10 u

Therefore, the ball reaches the ground in 1.79 u.

I hope it helps you!