Solve the problem.
-A rock is thrown vertically upward from the surface of an airless planet. It reaches a height of $\mathrm { s } = 120 \mathrm { t } - 4 \mathrm { t } ^ { 2 }$ meters in $t$ seconds. How high does the rock go? How long does it take the rock to reach its highest point?
A) 1800 m, 30 sec
B) 3480 m, 30 sec
C) 900 m, 15 sec
D) 1785 m, 15 sec

Question

Quizplus · Accepted Answer

To find the maximum height reached by the rock, we first need to find the time at which this height is achieved. This can be done by finding the vertex of the parabola described by the equation $s = 120t - 4t^2$. The time at which the maximum height is reached is given by $-b/(2a)$ from the vertex formula of a parabola, where $a = -4$ and $b = 120$. Thus, $t = -120 / (2 \times -4) = 15$ seconds. Substituting $t = 15$ back into the equation for $s$, we get $s = 120(15) - 4(15)^2 = 1800 - 900 = 900$ meters. Therefore, the rock reaches its highest point of 900 meters at 15 seconds.

Solve the Problem s=120t−4t2\mathrm { s } = 120 \mathrm { t } - 4 \mathrm { t } ^ { 2 }s=120t−4t2

Solve the Problem $\mathrm { s } = 120 \mathrm { t } - 4 \mathrm { t } ^ { 2 }$