A coin is tossed upward from a balcony $176 \mathrm{ft}$ high with an initial velocity of 16 feet per second. The height of the coin, in feet, after $t$ seconds is given by the function $h(t)=-16 t^{2}+16 t+176$. For what length of time will the coin be at a height of at least 80 feet?
A) $0 \mathrm{sec}$ to $3 \mathrm{sec}$
B) $3 \mathrm{sec}$ to $6 \mathrm{sec}$
C) $2 \mathrm{sec}$ to $3 \mathrm{sec}$
D) $0 \mathrm{sec}$ to $1 \mathrm{sec}$

Question

Quizplus · Accepted Answer

To find the time when the coin is at least 80 feet high, set the height function equal to 80 and solve for $t$: $-16t^2 + 16t + 176 = 80$. Simplifying gives $16t^2 - 16t - 96 = 0$, or $t^2 - t - 6 = 0$, which factors to $(t-3)(t+2) = 0$. The positive root is $t = 3$, indicating the coin reaches 80 feet on its way up and again on its way down at 3 seconds. Thus, the coin is at least 80 feet high from $0$ to $3$ seconds.

A Coin Is Tossed Upward from a Balcony 176ft176 \mathrm{ft}176ft High with an Initial Velocity of 16 Feet Per Second

A Coin Is Tossed Upward from a Balcony $176 \mathrm{ft}$ High with an Initial Velocity of 16 Feet Per Second