Question

A toy rocket is shot vertically into the air from a launching pad 3 feet above the ground with an initial velocity of 112 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 + 112t + 3. How long will it take the rocket to reach its maximum height? What is the maximum height? The rocket reaches its maximum height at ___ second(s) after launch.The maximum height reached by the object is ___ feet.

Answer 1

The rocket reaches its maximum height at 3.5 seconds after launch.

The maximum height reached by the objec

Step-by-step explanation

The maximum of a function can be found out by taking the first derivative of that function.

At the maximum point, the first derivative of the function is 0 and the second derivative is negative.

h(t) = -16t² + 112t + 3

(dh/dt) = -32t + 112 = 0

-32t = -112

Divide both sides by -32

(-32t/-32) = (-112/-32)

t = 3.5 s

(d²h/dt²) = -32

This confirms that the value obtained from the first derivative is for the maximum height

For the second part, we will substitute t = 3.5 s

h(t) = -16t² + 112t + 3

h(t = 3.5) = -16 (3.5²) + 112 (3.5) + 3 = -196 + 392 + 3 = 199 ft

Hope this Helps!!!