h= -16t^2+100t+84

Question

Benjamin threw a rock straight up from a cliff that was 84 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation h= -16t^2+100t+84, how long will it take for the rock to hit the water?(answer in seconds)

Answer 1

The rock will hit the water when h = 0  ==>  

 

-16t^2 + 100t + 84 = 0

4t^2 - 25t - 21 = 0

(4t + 3)(t - 7) = 0  

t = -3/4  or  t = 7  

 

A negative time does not make sense in this problem so discard t = -3/4  

 

The rock will hit the water in 7 seconds  

 

Check:  h(7) = -16(7^2) + 100(7) + 84 = -784 + 700 + 84 = 0