Question

A baseball is thrown into the air from a height of 5 feet. The ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. Which equation models the height of the baseball? Assume that acceleration due to gravity is –16 ft/s2.

h(t) = 16t2 + 49.64t + 5
h(t) = -16t2 + 5t + 49.64
h(t) = -16t2 + 49.64t + 5
h(t) = 16t2 + 5t + 49.64

Answer 1

Use h(t) = -16t^2 + v0 t + 5 (acceleration -16, initial height 5). The time to the vertex is t_peak = v0/(32). At the vertex h = 43.5, so

-16(v0/32)^2 + v0(v0/32) + 5 = 43.5
=> v0^2/64 = 38.5 => v0^2 = 2464 => v0 ≈ 49.64 ft/s.

Thus the model is h(t) = -16t^2 + 49.64t + 5 (third choice).