Applications of quadratics. Rock

Question

A boy threw a rock straight up from my Clift that was 24 feet above the water. If the height of the rock, h, in feet, after 1 seconds is given by the equation h= -16t + 20t + 24, how long will it take for the rock to hit the water? 

The rock will take___seconds to hit the water

Answer 1

You didn't quite give the correct equation for the height.  It should be:

 

     h(t) = -16t² + 20t + 24

 

When the rock hits the water, its height will be zero, so you have:

 

     0 = -16t² + 20t + 24

 

Divide both sides by -4:

     0 = 4t² - 5t - 6

Factor using the ac method:

     0 = 4t² - 8t + 3t - 6

     0 = 4t(t-2) + 3(t-2)

     0 = (4t+3)(t-2)

 

So t = -3/4 and 2.  Since we can't go back in time, t = 2 seconds.  To check it, plug t = 2 back into the h(t) equation and verify that h(2) = 0.