Solve the problem.
-A ball dropped from the top of a building has a height of $s = 576 - 16 \mathrm { t } ^ { 2 }$ meters after $\mathrm { t }$ seconds. How long does it take the ball to reach the ground? What is the ball's velocity at the moment of impact?
A) $36 \mathrm { sec } , - 1152 \mathrm {~m} / \mathrm { sec }$
B) $6 \mathrm { sec } , 192 \mathrm {~m} / \mathrm { sec }$
C) $12 \mathrm { sec } , - 96 \mathrm {~m} / \mathrm { sec }$
D) $6 \mathrm { sec } , - 192 \mathrm {~m} / \mathrm { sec }$

Question

Quizplus · Accepted Answer

To find the time it takes for the ball to reach the ground, set $s = 0$ and solve for $t$: $0 = 576 - 16t^2$, which gives $t = 6$ seconds. To find the velocity at impact, differentiate $s$ with respect to $t$ to get $v = ds/dt = -32t$, and substitute $t = 6$ to get $v = -192 \, \text{m/s}$.

Solve the Problem s=576−16t2s = 576 - 16 \mathrm { t } ^ { 2 }s=576−16t2

Solve the Problem $s = 576 - 16 \mathrm { t } ^ { 2 }$