quadradics problem

Question

a stone is thrown downward from the top of a building with an initial speed of 15 feet per second: the distance d in feet that it falls in t seconds is d=16t2 +15t. How many seconds will it take for the rock to go  a distance of 162 feet?

Answer 1

d = (1/2)at² + v_it

 

162 = 16t² + 15t

 

16t² + 15t - 162 = 0

 

Use quadratic equation:  t = [-b ±√(b²-4ac)]/2a  with a=16, b=15, c= -162

 

t = [-15 ±√(15²-4(16)(162))]/32

 

t = (-15 ±√10593)/32

 

t = (-15 ± 102.9223)/32

 

We can disregard the negative so t = (-15 + 102.9223)/32

 

t = 2.7476 seconds....

 

Rounded to 2 decimal places it takes 2.75 seconds to travel 162 feet