Question

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second then its height H after T seconds is given by the equation h(t)=-16t^2+128t (if air resistance is neglected). When will the object reach its maximum height?
A. 8 seconds
B. 6 seconds
C. 0 seconds
D. 4 seconds​

Answer 1

We have been given that a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second then its height H after T seconds is given by the equation $h(t)=-16t^2+128t$ (if air resistance is neglected).

We are asked to find the time when the object will reach its maximum height.

We can see our given equation is a downward opening parabola, so its maximum point will be vertex of parabola.

We know that x coordinate of vertex is $\frac{-b}{2a}$.

We can see from our given equation that $b=128$ and $a=-16$.

$\frac{-b}{2a}=\frac{-128}{2(-16)}=\frac{-128}{-32}=4$

Therefore, the object will reach its maximum height after 4 seconds and option D is the correct choice.