Question

Suppose a rock is thrown off of a bridge into the river 120 feet below. The height, h, in feet of the rock above the river is given by h = ?16t2 + 84t + 120, where t is the time in seconds. How long does it take the rock to splash into the river below?

Answer 1

6.4

Explanation:

Answer 2

about 6.418 seconds

Explanation:

You apparently want to find t when h=0:

0 = -16t^2 +84t +120

0 = 4t^2 -21t -30 . . . . . . divide by -4

t = (-(-21 ±√((-21)² -4(4)(-30)))/(2(4)) = (21±√921)/8 . . . . only the positive time is of interest

t = 2.625+√14.390625 ≈ 6.419 . . . . seconds

It takes about 6.42 seconds for the rock to hit the water.