The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds.

Question

The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t² + 96t, where t is the time in seconds. 

a) How long will it take the object to reach a height of 144 feet?   SHOW WORK

b) How long will it take the object to return to the point of departure?  SHOW WORK

Answer 1

144 = -16t^2 +96t

16t^2 -96t + 144 = 0

divide by 16

t^2 -6t + 9 =0

factor

(t-3)^2 = 0

t-3=0

t = 3 seconds to reach 144 feet (which is the maximum height)

-16t^2+96t =0

t^2 -6t =0

t(t-6) = 0

t =6 seconds to return