Solve.
-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, $\mathrm { d }$, after $t$ seconds may be found by the formula $d = - 16 t ^ { 2 } + 40 t + 50$. 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 $= 75 \mathrm { ft }$; time to reach ground $= 1.25$ seconds
B) Maximum height $= 75 \mathrm { ft }$; time to reach ground $= 2.5$ seconds
C) Maximum height $= 50 \mathrm { ft }$; time to reach ground $= 2.5$ seconds
D) Maximum height $= 50 \mathrm { ft }$; time to reach ground $= 1.25$ seconds

Question

Quizplus · Accepted Answer

The maximum height can be found by using the vertex formula for a parabola, $h = -\frac{b}{2a}$, where $a = -16$ and $b = 40$. Plugging these values in gives the time to reach maximum height as $t = \frac{40}{2 \times 16} = 1.25$ seconds. The maximum height is then found by plugging $t = 1.25$ into the original equation, yielding $d = -16(1.25)^2 + 40(1.25) + 50 = 75$ feet. To find the time it takes to fall back to the ground, we set $d = 0$ and solve for $t$, which gives $t = 2.5$ seconds, indicating it takes 2.5 seconds for the object to hit the ground.

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

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-A Person Is Standing on the Top of a Building