Question

A rocket is fired upward from some initial distance above the ground. Its height (in feet), h, above the ground t seconds after it is fired is given by h(t)=−16t2+112t+128. What is the rocket's maximum height?

Answer 1

the object will attain maximum height at 3.5 seconds.

Explanation:

The height of the object (in feet), h, above the ground t seconds after it is fired is given by h(t)=−16t2+112t+128.

128 represents 128 feet above the ground and this is the height from which the object was fired.

The given equation is a quadratic equation and plotting of this equation on a graph would give a parabola whose vertex would be equal to the maximum height travelled by the rocket.

The vertex of the parabola is calculated as follows,

Vertex = -b/2a

From the equation,

a = -16

b = 112

Vertex = - - 112/32= 3.5

So the object will attain maximum height at 3.5 seconds.