Story Problem for Calculus

Question

A ball is thrown in the air.  The height of the ball is given by the equation h(t)=-16t^2+30t, where t is the time in seconds.  How long will it take for the ball to hit the ground, h(t)=0, rounded to the nearest hundredth of a second.

Answer 1

Another way to solve the problem. Your function has the first coefficient with negative sign,

which means it may only maximum. The time the ball reaches the ground is double of the time needed to reach to its maximum position. To find that time just calculate derivative of your function and make it equal zero. It gives you

 

                  h'(t) = - 32t + 30 = 0    or t = 15/16

 

Time you need is

 

                               t = 2x15/16 = 15/8 seconds

Answer 2

when the ball hits the ground, height is zero, therefore

 

0 = -16t² +30t

 

2t(8t - 15) = 0

 

8t = 15

 

t = 15/8 seconds