Solve the problem.
-Consider the quadratic model h(t) = -16t2 + 40t + 50 for the height (in feet), h, of an object t seconds after the object has been projected straight up into the air. Find the maximum height attained by the object. 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 = 2.5 seconds
C) maximum height = 75 ft; time to reach ground = 1.25 seconds
D) maximum height = 50 ft; time to reach ground = 2.5 seconds

Question

Quizplus · Accepted Answer

The maximum height can be found by using the vertex formula for a quadratic equation, $ h(t) = -16t^2 + 40t + 50 $. The time at the vertex, $ t_v $, is given by $ t_v = -\frac{b}{2a} = -\frac{40}{2(-16)} = 1.25 $ seconds. Plugging $ t_v $ back into the equation gives the maximum height, $ h(1.25) = -16(1.25)^2 + 40(1.25) + 50 = 75 $ feet. To find the time it takes to hit the ground, set $ h(t) = 0 $ and solve for $ t $, which gives two solutions, one of which is $ t = 2.5 $ seconds (the other solution is the start time, $ t = 0 $). This accounts for the time up and down, confirming the object takes 2.5 seconds to hit the ground after being projected.

Solve the Problem. -Consider the Quadratic Model H(t) = -16t2 + 40t