Solve the problem.
-A person is standing on the top of a building 50 feet above the ground. They project an object upward with an initial velocity of 40 feet per second. The object's distance above the ground, d, after t seconds may be found by
The formula d = -16t2 + 40t + 50. What is the maximum height the object will reach. How much time does it take
To fall back to the ground? Assume that it takes the same time for going up and coming down.
A)maximum height = 50 ft; time to reach ground = 1.25 seconds
B)maximum height = 75 ft; time to reach ground = 1.25 seconds
C)maximum height = 75 ft; time to reach ground = 2.5 seconds
D)maximum height = 50 ft; time to reach ground = 2.5 seconds

Question

Quizplus · Accepted Answer

To find the maximum height, we need to find the vertex of the parabolic equation -d = -16t^2 + 40t + 50. The vertex is given by t = -b/2a = -40/-32 = 1.25 seconds. Substituting this value in the equation, we get d = -16(1.25)^2 + 40(1.25) + 50 = 75 feet. 
To find the time taken to fall back to the ground, we need to find the time when the object will hit the ground. This is given by the positive root of the equation -16t^2 + 40t + 50 = 0, which is t = (-(40) ± sqrt((40)^2 - 4(-16)(50))) / (2(-16)) = 2.5 seconds. Therefore, the answer is C.

Solve the Problem. -A Person Is Standing on the Top of a Building