Question

A rock is strong from the top of a tall building. the distance in feet between the rock in the ground x seconds after it is their own is given by f(x)=-16x2-4x+ 382 how long after the rock is thrown is it 340 feet from the ground

Answer 1

1.5 seconds.

Explanation:

f(x) = -16t^2 - 4x + 382

At 340 ft from the ground:

-16t^2 - 4x + 382 = 340

-16t^2 - 4x + 42 = 0

-2(8t^2 + 2x - 21) = 0

8 * -21 = -168 and we need 2 numbers whose product is -168 and sum = +2.

These are 14 and -12 se we write:

8t^2 - 12x + 14x - 21 = 0

4x( 2x - 3) + 7(2x - 3) = 0

(4x + 7)(2x - 3) = 0

x = -7/4, 3/2

so x = 1.5 seconds.