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=-16

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+28t+60 how long will it take the rock to hit the water?

Answer 1

Set h=0

 

 

0 = -16t² + 28t + 60

0 = -4(4t² - 7t - 15)

 

 

Set the term in parenthesis equal to zero.

 

4t² - 7t - 15 = 0

 

(4t + 5)(t  - 3) = 0

 

 

Set the factors equal to zero.

 

4t + 5 = 0             and              t - 3 = 0

 

4t = -5                 and              t = 3

 

t = -1.25

 

 

We take the positive value of t.

 

The time it takes is 3 seconds.