if a ball is thrown in the air and the equation is h = -16t^2 + 64t + 8. t is time and h is height. How long will it take to reach 3 feet?

Question

Can you please describe when the ball will be at a height of 3 feet after it is thrown?

Answer 1

 

Hi Greg,

 

The equation can be transformed as follows

 

     h(t) = -16t² + 64t + 8

 

           = -16(t² - 4t) + 8

 

           = -16(t² - 4t + 4 - 4) + 8

 

           = -16(t² - 4t + 4) + (64 + 8)

 

           = -16(t - 2)² + 72      (Eq. 1)

 

which says the ball will reach its maximum height of 72 feet when t = 2.

 

So, the ball thrown up at a height of 8 feet ( h(0) = 8 )

 

will reach up to 72 feet and 

 

then will be falling according to Eq. 1 above.

 

If we solve h(t) = 3

 

     -16(t - 2)² + 72 = 3

 

     16(t - 2)² = 69

 

     (t - 2)² = 69/16

 

     t - 2 = ±√(69/16)

 

     t = 2 ± √(69/16)

 

     t = 4.0767   or t = -0.0767

 

t = -0.0767 is meaningless here, and

 

the ball will be at a height of 3 feet in 4.0767 sec after it has been thrown.