Solve the problem.
-A coin is tossed upward from a balcony $300 \mathrm { ft }$ high with an initial velocity of $32 \mathrm { ft } / \mathrm { sec }$. During what interval of time will the coin be at a height of at least $60 \mathrm { ft }$ ? $\left( h = - 16 \mathrm { t } ^ { 2 } + \mathrm { v } _ { \mathrm { O } } \mathrm { t } + \mathrm { h } _ { \mathrm { O } } \right.$.)
A) $0 \leq t \leq 5$
B) $4 \leq \mathrm { t } \leq 5$
C) $5 \leq t \leq 10$
D) $0 \leq t \leq 1$

Question

Quizplus · Accepted Answer

The equation for the height of the coin at any time $t$ is given by $h = -16t^2 + 32t + 300$. To find when the coin is at least 60 ft high, we set $h \geq 60$ and solve for $t$: $-16t^2 + 32t + 300 \geq 60$. Simplifying gives $-16t^2 + 32t + 240 \geq 0$, which factors to $-16(t^2 - 2t - 15) \geq 0$, or $t^2 - 2t - 15 \leq 0$. Factoring or using the quadratic formula gives the roots as $t = -3$ and $t = 5$, but since time cannot be negative, we only consider $0 \leq t \leq 5$.

Solve the Problem 300ft300 \mathrm { ft }300ft High with an Initial Velocity Of

Solve the Problem $300 \mathrm { ft }$ High with an Initial Velocity Of