solve using quadratic equation, question below

Question

A ball is thrown downward from a window in a tall building. Its position at time (t) in seconds is s=16ft^2+32ft where s is in feet. How long(to the nearest tenth)_will it take the ball to fall 68ft?

Answer 1

s(t) = 16t² + 32t

 

We want s(t) = 68, so:

 

68 = 16t² + 32t

0 = 16t² + 32t - 68

0 = 4t² + 8t - 17          {Divided both sides by 4}

 

Use the quadratic formula, t = (-b/2a) ± (1/2a)√(b²-4ac).  Here a=4, b=8, c=-17:

 

t = -8/(2)(4) ± (1/8)√{8²-(4)(4)(-17)}

t = -1 ± (1/2)√21

t ≅ -3.3 and 1.3 seconds   (rounded to nearest tenth)

 

Since -3.3 seconds is in the past, the answer is t = 1.3 seconds.

 

Check:

s(t=1.29) = 16(1.3)² + 32(1.3)

= 16(1.66) + 32(1.3)

= 68.6    close enough with rounding