Answer:
29 feet
2.6 seconds
Step-by-step explanation:
h(t) is a downwards parabola, so the maximum is at the vertex.
t = -b / (2a)
t = -40 / (2×-16)
t = 1.25
h(1.25) = -16(1.25)² + 40(1.25) + 4
h(1.25) = 29
When the ball lands, h(t) = 0.
0 = -16t² + 40t + 4
0 = 4t² − 10t − 1
t = [ -(-10) ± √((-10)² − 4(4)(-1)) ] / 2(4)
t = (10 ± √116) / 8
t = (5 ± √29) / 4
t is positive, so:
t = (5 + √29) / 4
t ≈ 2.6
