Question

3. Derek throws a baseball upward from an initial height of 3 ft. The baseball hits the ground after 2 seconds.

a. What was the initial velocity of the baseball?
b. What is the function that models the height, ℎ (in feet), of the baseball over a period of time tt (in seconds)?
c. At what time did the baseball reach its maximum height? What was the maximum height of the baseball?

Answer 1

Answer with Step-by-step explanation:

Since we have given that

Initial height = 3 feet

The baseball hits the ground after 2 seconds

t = 2 seconds

So, final velocity = v = 0

a. What was the initial velocity of the baseball?

Initial velocity is given by

`v_0=(3)/(2)=1.5\ ft/sec`

b. What is the function that models the height, ℎ (in feet), of the baseball over a period of time tt (in seconds)?

As we know that the function of height would be

`h(t)=-16t^2+v_0t+h_0`

Here,
`h_0` is the initial height.

So, our function becomes,

`h(t)=-16t^2+1.5t+3`

c. At what time did the baseball reach its maximum height? What was the maximum height of the baseball?

Maximum height at time t:

`t=(-b)/(2a)=(-1.5)/(2* -16)=(1.5)/(32)\approx 0.05\ seconds`

Maximum height would be

`h(0.05)=-16(0.05)^2+1.5* 0.05+3=3.035\ ft`