Polynomials

Question

The height h, in feet, of an airborn tee-shirt t seconds after being launched can be approximated by h=-15t²+135t+10, 0<= t <=10. Find the times when the shirt will reach a fan 220 feet above ground level.

 

Answer 1

Hi Dyana,

Since the height is 220 feet, we substitute 220 in for h, then solve the polynomial.

 

220 = -15t²+135t+10

 

Put the 220 on the right side so the left side =0

 

0 = -15t²+135t-210

 

To simplify things, I am going to divide every term on both sides by -15,  this gives me

 

t²-9t+14 = 0

 

This factors into (t-2)(t-7)=0

 

So t-2 = 0  or  t-7=0

 

or  at t=2 seconds the t-shirt reaches a fan on the way up  and

 

at t=7 seconds the t-shirt reaches a fan on the way back down.