0 = -16t ^ 2 + 32t + 48
Part A:
Factoring we have:
0 = -16 (t ^ 2 - 2t + -3)
0 = (t ^ 2 - 2t + -3)
0 = (t + 1) * (t-3)
t> 0
t-3 = 0
t = 3
Answer:
The ball is in the air for 3 s.
Part B:
h (t) = - 16t ^ 2 + 32t + 48
We evaluate for t = 1
h (1) = - 16 * (1) ^ 2 + 32 * (1) + 48
h (1) = 64
Answer:
The height of the ball at 1 second is:
h (1) = 64 feet
Part C:
We derive the equation and we equate to zero:
h '(t) = - 32t + 32
0 = -32t + 32
32t = 32
t = 1
h '' (t) = - 32 <0 (t = 1 is a maximum)
Answer:
Yes, The ball at its maximum height at t = 1 second.
