Benjamin threw a rock straight up from a cliff

Question

 Benjamin threw a rock straight up from a cliff that was 60 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation h=-16t^2+68t+60, how long will it take for the rock to hit the water?

Answer 1

h(t) = 0 = -16t^2 + 68t + 60

4t^2 - 17t -15 =0

factor

(4t+3)(t-5) = 0 set the factors equal to zero and solve for t

t =5 and -3/4 of a second ignore the negative solution

h(3/4) = -16(5)^2 + 68(5) + 60= -400 + 340 +60 = 0

it takes 5 seconds for it to hit the ground