Question

A firecracker shoots up from a hill 140 feet high with an initial speed of 100 feet per second. Using the formula H(t) = -16t2 + vt + s, approximately how long will it take the firecracker to hit the ground?
Answer
5 seconds
7 seconds
9 seconds
11 seconds
HELP D;

Answer 1

H(t) = -16t^2 + vt + s


H(t) = -16t^2 + 100t + 140


0 = -16t^2 + 100t + 140


-16t^2 + 100t + 140 = 0


-4(4t^2 - 25t - 35) = 0


-4(4t^2 - 25t - 35) = 0


4t^2 - 25t - 35 = 0/(-4)


4t^2 - 25t - 35 = 0


Now use the quadratic formula to solve for t


t = (-b+-sqrt(b^2-4ac))/(2a)


t = (-(-25)+-sqrt((-25)^2-4(4)(-35)))/(2(4))


t = (25+-sqrt(625-(-560)))/(8)


t = (25+-sqrt(1185))/8


t = (25+sqrt(1185))/8 or t = (25-sqrt(1185))/8


t = 7.42797 or t = -1.17797


So it will take roughly 7 seconds for the firecracker to hit the ground.