a small rocket is launched vertically upward from the edge of a cliff 400 ft off the ground at the speed of 200 ft/s. its height above the ground is given by the function h(t)

Question:

A small rocket is launched vertically upward from the edge of a cliff 80 ft off the ground at a speed of 69 ft/s. Its height (in feet) above the ground is given by   where t represents time measured in seconds.

Assuming the rocket is launched at t=0, what is an appropriate domain for h?

Explanation:

Given

Required

Determine the domain of h

The initial value of t is 0.

i.e.

--- This is given in the question

To determine the final value, we simply solve for t in

Rewrite the expression:

Divide through by -25

Using quadratic formula:

Where

     and

The expression becomes:

So, we have:

Split

But time can't be negative.

So:

Hence, the domain is: