Solve the problem.
-Consider the quadratic model h( $$h ( t ) = - 16 t ^ { 2 } + 40 t + 50$$ 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 using the vertex formula for a quadratic equation, $$h = -\frac{b}{2a}$$, where $a = -16$ and $b = 40$. Plugging these values in gives the time to reach maximum height as $$t = -\frac{40}{2(-16)} = 1.25$$ seconds. The maximum height is then found by plugging this time back into the original equation, yielding $$h(1.25) = -16(1.25)^2 + 40(1.25) + 50 = 75$$ feet. To find the time it takes to hit the ground, we set $h(t) = 0$ and solve for $t$, which gives two solutions, one of which is $t = 0$ (the start) and the other is the time it hits the ground. Solving this gives a time of $2.5$ seconds to hit the ground.

Solve the Problem h(t)=−16t2+40t+50h ( t ) = - 16 t ^ { 2 } + 40 t + 50h(t)=−16t2+40t+50

Solve the Problem $h ( t ) = - 16 t ^ { 2 } + 40 t + 50$