Question

A toy rocket is shot vertically into the air from a launching pad 4 feet above the ground with an initial velocity of 88 feet per second. The height​ h, in​ feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16t^2+88t+4 How long will it take the rocket to reach its maximum​ height? What is the maximum​ height?

Answer 1

To find the time it takes for the rocket to reach its maximum height, we need to determine the time at which the vertex of the parabolic function occurs. The function h(t) is in the form of a quadratic equation, h(t) = at^2 + bt + c, where a = -16, b = 88, and c = 4.

The time at which the vertex occurs can be found using the formula t = -b/(2a). Plugging in the values, we have t = -88/(2*-16) = 11/4 seconds.

To find the maximum height, we substitute the value of t = 11/4 into the function h(t):
h(11/4) = -16(11/4)^2 + 88(11/4) + 4
= -484/16 + 968/4 + 4
= 242/8 + 968/4 + 4
= 124 + 968/4
= 124 + 242
= 366 feet.

Therefore, the rocket will reach its maximum height in 11/4 seconds, and the maximum height is 366 feet.