Answer:
1. What is the initial height of the baseball?
To find the initial height of the baseball, we need to evaluate g(0) since 0 seconds after it was hit represents the initial time.
g(0) = (-16(0) - 1)(0 - 4) = (-1)(-4) = 4
Therefore, the initial height of the baseball is 4 feet.
2. What is the maximum height reached by the baseball and when does it occur?
To find the maximum height reached by the baseball, we need to find the vertex of the parabola represented by g(t). The vertex occurs at t = -b/2a, where a and b are coefficients in standard form (ax^2 + bx + c).
In this case, a = -16 and b = -15.
t = -b/2a = -(-15)/(2(-16)) = 15/32
To find the maximum height, we substitute t = 15/32 into g(t):
g(15/32) = (-16(15/32) - 1)(15/32 - 4) ≈ 10.67
Therefore, the maximum height reached by the baseball is approximately 10.67 feet and it occurs at t ≈ 0.47 seconds.
3. When does the baseball hit the ground?
The baseball hits the ground when its height is equal to zero. So we need to solve for t when g(t) = 0:
(-16t - 1)(t - 4) = 0
This equation is true when either (-16t -1) or (t-4) equals zero.
Solving for (-16t-1)=0 gives us t=-1/16 which is not a valid solution since time cannot be negative.
Solving for (t-4)=0 gives us t=4 which means that after hitting it takes exactly four seconds for ball to hit ground.
Therefore, the baseball hits the ground after exactly four seconds from being hit by Player B