If a ball is thrown into the air with a velocity of $58 \mathrm { ft } / \mathrm { s }$, its height (in feet) after $t$ seconds is given by
$$H = 58 t - 9 t ^ { 2 } .$$
Find the velocity when $t = 9$.
A) $- 101 \mathrm { ft } / \mathrm { s }$
B) $- 104 \mathrm { ft } / \mathrm { s }$
C) $- 106 \mathrm { ft } / \mathrm { s }$
D) $- 103 \mathrm { ft } / \mathrm { s }$
E) $- 99 \mathrm { ft } / \mathrm { s }$

Question

Quizplus · Accepted Answer

The velocity is the derivative of the height function $H = 58t - 9t^2$. The derivative is $v(t) = 58 - 18t$. Substituting $t = 9$, we get $v(9) = 58 - 18 \times 9 = -104 \mathrm{ ft/s}$.

If a Ball Is Thrown into the Air with a Velocity