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
[tex]v_0=\dfrac{3}{2}=1.5\ ft/sec[/tex]
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
[tex]h(t)=-16t^2+v_0t+h_0[/tex]
Here, [tex]h_0[/tex] is the initial height.
So, our function becomes,
[tex]h(t)=-16t^2+1.5t+3[/tex]
c. At what time did the baseball reach its maximum height? What was the maximum height of the baseball?
Maximum height at time t:
[tex]t=\dfrac{-b}{2a}=\dfrac{-1.5}{2\times -16}=\dfrac{1.5}{32}\approx 0.05\ seconds[/tex]
Maximum height would be
[tex]h(0.05)=-16(0.05)^2+1.5\times 0.05+3=3.035\ ft[/tex]
