Question

A cliff diver dives into the water from an overlook. His height in feet is given by y(t) = −16t2 + 32t + 84, where t is the time in seconds. The horizontal distance in feet of the diver from the overlook is given by x(t) = 2t. What horizontal distance will the diver travel before he hits the water?

Answer 1

7 feet

Explanation:

The time the diver is in air is the solution to y(t) = 0.

-16t^2 +32t +84 = 0

Dividing by -4, we can simplify this to ...

4t^2 -8t -21 = 0

(2x +3)(2x -7) = 0 . . . . factor

Solutions are x = -3/2, x = 7/2. Only the positive one makes any sense in this problem.

Then the horizontal distance is x(t) = 2t, so x(7/2) = 2(7/2) = 7 feet.