Solve the problem.
-A coin is tossed upward from a balcony $176 \mathrm { ft }$ high with an initial velocity of $16 \mathrm { ft } / \mathrm { sec }$. During what interval of time will the coin be at a height of at least $80 \mathrm { ft }$ ? $\left( \mathrm { h } = - 16 \mathrm { t } ^ { 2 } + \mathrm { v } _ { 0 } \mathrm { t } + \mathrm { h } _ { 0 } \right.$.)
A) $3 \leq t \leq 6$
B) $2 \leq t \leq 3$
C) $0 \leq t \leq 3$
D) $0 \leq t \leq 1$

Question

Quizplus · Accepted Answer

The equation for the height of the coin is $ h(t) = -16t^2 + 16t + 176 $. Setting $ h(t) \geq 80 $, we solve the inequality: $-16t^2 + 16t + 176 \geq 80$. Simplifying gives $-16t^2 + 16t + 96 \geq 0$. Solving the quadratic equation $-16t^2 + 16t + 96 = 0$ gives roots $t = -2$ and $t = 3$. The coin is at least 80 ft high between $0 \leq t \leq 3$.

Solve the Problem 176ft176 \mathrm { ft }176ft High with an Initial Velocity Of

Solve the Problem $176 \mathrm { ft }$ High with an Initial Velocity Of