Problema Solution
A toy rocket is shot vertically into the air from a 9-foot-tall launching pad with an initial velocity of 128 feet per second. Suppose the height of the rocket in feet t seconds after being launched can be modeled by the function h left parenthesis t right parenthesis equals negative 16 t squared plus v 0 t plus h 0h(t)=−16t2+v0t+h0, where v 0v0 is the initial velocity of the rocket and h 0h0 is the initial height of the rocket. How long will it take for the rocket to reach its maximum height? What is the maximum height?
Answer provided by our tutors
h(t)=−16t^2+v0t+h0
h0 = 9 ft
v0 = 128 ft/s
h(t) = -16t^2 + 128t + 9
We need to find the vertex of the parabolic function h(t) = -16t^2 + 128t + 9:
t max = -b/2a, a = -16, b = 128, c = 9
t max = -128/2*(-16)
t max = 4 s
h max = c - b^2/(4a)
h max = 9 - 128^2/(4*(-16))
h max = 265 ft
The rocket will reach the maximum height in 4 seconds.
The maximum height of the rocket is 265 feet.