Chapter 6.3, Problem 68E

Sledding The time in seconds that it takes for a sled to slide down a hillside inclined at an angle θ is

$t=\sqrt{\frac{d}{16\sin \theta }}$

where d is the length of the slope in feet. Find the time it takes to slide down a 2000-ft slope inclined at 30°.

To determine

To find: The time taken to slide down a $2000\text{ft}$ slope inclined at $30°$.

Answer to Problem 68E

The time taken to slide down a $2000\text{ft}$ slope inclined at $30°$ is $16\sec$.

Explanation of Solution

Given:

A sliding slope of length $2000\text{ft}$ at an angle $30°$ is given.

Calculation:

Formula to find the time, $\left(t\right)$ taken to slide down a distance $d$ at angle $\theta$.

$t=\sqrt{\frac{d}{16\sin \theta }}$

Substitute $2000$ for $d$ and $30°$ for $\theta$.

$\begin{array}{c}t=\sqrt{\frac{2000}{16\sin 30°}}\\ =\sqrt{\frac{2000}{16\times \frac{1}{2}}}\left(\sin 30°=\frac{1}{2}\right)\\ =15.81\\ \approx 16\end{array}$

Therefore, the time taken to slide down a slope of length $2000\text{ft}$ inclined at angle $30°$ is $16\sec$.