how many seconds will it take for the ball to reach the bottom of the pole?

Question

della's parents are throwing a Sweet 16 party for her. At 10:00, a ball will slide 25 feet down a pole and light up. A function that models the drop is h=t^2+5t+25, where h is height in feet of the ball after t seconds. How many seconds will it take for the ball to reach the bottom of the pole? 

Answer 1

Hi Leah,

This is an algebra problem, pure and simple.  The trick is to recognize that h=0 at the moment that the ball reaches the bottom of the pole (h is a function that describes the height of the ball above the ground).

 

If we set h=0, then

 

0 = -(t^2) + 5*t + 25

 

To solve for t, you'll need to use the 'quadratic equation' (dun dun DUNN!!!!).  I suspect this was covered in class, and is likely in your textbook.  In the formula for the quadratic equation, there are variables 'a', 'b', and 'c', which you'll need to identify as coefficients from the equation above.  Plug these coefficients into the quadratic equation, and "boom", you've got your answer (Note: you may get two answers from the quadratic equation because it involves a square root.  However, t must be positive.  Negative time makes no sense!!)

 

Hope this helps!

 

Paul