when will the football pass the top of the bleachers? and when will the football hit hte ground? s=0. please show work

Question

a ball is thrwoing vertically upward from the top of a 14.7 meter set of bleachers. the hight of the football, s, in meters after t seconds is given by the fomula S=-4.9t^2+9.8t+14.7.... when will the football pass the top of the bleachers? and when will the football hit hte ground? s=0. please show work

Answer 1

Presumably when you say "when will the football pass the top of the bleachers?" you mean on the way down?

 

At that point, the football will be at a height of 14.7, the height of the bleachers.  So take the formula for the height and set it equal to 14.7, and see what happens.

 

14.7 = -4.9t²+9.8t+14.7

0 = -4.9t²+9.8t

0 = t(-4.9t + 9.8)

 

This equation is true when t = 0 and when -4.9t + 9.8 = 0.  Solve the second equation:

 

-4.9t + 9.8 = 0

9.8 = 4.9t

2 = t.

 

So the ball is at the top of the bleachers when t = 0 and when t = 2.  t = 0 is when the ball was originally thrown, so that's not the answer to the question.  So t = 2 seconds is the time at which the ball will pass the top of the bleachers on the way down.

 

To find the time when the ball hits the ground, set the formula for height to 0 and solve that:

 

0 = -4.9t²+9.8t+14.7

 

Divide both sides by -4.9:

0 = t² - 2t -3

0 = (t-3)(t+2)

 

So t = 3 or t = -2.

 

t = -2 is before the ball was thrown, so that can't be right.  But t = 3 makes sense.  So the ball will hit the ground after 3 seconds.