Question

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function f (x) = negative 15 t squared + 48 t, where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height in feet. What is the maximum height the rocket reaches?
16 ft
36 ft
48 ft
144 ft

Answer 1

Using the vertex of a parabola, t = -b/(2a).

If the model were f(t) = -16t^2 + 48t (usual gravity approximation), t = 48/(32) = 1.5 s and f(1.5) = -16(1.5)^2 + 48(1.5) = 36 ft.

(If you use the given -15 coefficient, the vertex is at t = 48/(30) = 1.6 s and f(1.6) = 38.4 ft, which is not one of the choices.)

Answer: 36 ft.