13/8 word prob

Question

An object is thrown downward with an initial velocity of
4
feet per second. The relationship between the distance
s
it travels and time
t
is given by
s=4t+16t2
. How long does it take the object to fall
72
feet?

Answer 1

s(t) = 16t² + 4t

 

Set s(t) = 72 and solve the resulting quadratic equation for t.

 

72 = 16t² + 4t

 

16t² + 4t - 72 = 0

 

Divide through by 4 to simplify it a little and get

 

4t² + t - 18 = 0

 

t = (1/8) [-1 ± √(1 + 4*4*18)] = (1/8)(-1 ± 17)

 

Keep only the positive t.

 

t = (1/8)(-1 + 17) s = 2s