the function h(t)=-5t(squared) +34t +7. A)roots? 0=-5t(squared) +34t +7? B) how long does it take for the ball to hit the ground?

Question

A baseball batter hits a line drive. The height, h, in metres ,of the baseball after t seconds is approximately modelled by the function h(t)=-5t(squared) +34t +7. A) what are the roots modelled by the function 0=-5t(squared) +34t +7? B) how long does it take for the ball to hit the ground?

Answer 1

-5t² + 34t + 7 = 0

(-5t - 1)(t - 7) = 0  

-5t - 1 = 0  or  t - 7 = 0  

t = -1/5  and  t = 7  are the roots of the function  

 

The ball will hit the ground when its height is 0, which is when h(t) = 0, which correspond to the roots of the equation.  But in this problem a negative time doesn't make sense so that root is discarded, which means the ball will hit the ground after 7 seconds.  

 

Check:  h(7) = -5*7² + 34*7 + 7 = -245 + 238 + 7 = 0