Question

The rocket reaches its maximum height at second(s) after launch. (Simplify your answer.) Save A toy rocket is shot vertically into the air from a launching pad 4 feet above the ground with an initial velocity of 40 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)= - 16t² + 40t+4. How long will it take the rocket to reach its maximum height? What is the maximum height.​

Answer 1

Explanation:

The function H(t) = -16t^2 + 64t + 9 is a quadratic function, whose plot is a parabola opened down.

This quadratic function has the maximum at the value of its argument t = -b%2F%282a%29, where "a" is the coefficient at t^2

and "b" is the coefficient at t.

In your case, a= -16, b= 64, so the function gets the maximum at t = -64%2F%282%2A%28-16%29%29 = 2 seconds.

So, the ball gets the maximum height 2 seconds after is hit straight up.

The maximum height is H(t) = -16*2^2 + 64*2 + 9 = 73 ft.