Question

A ladder is resting with the wall at an angle of $30$ degrees. A man is ascending the ladder at the rate of $3$ ft/sec.

His rate of approaching the wall is

• A. $3$ ft/sec
• B. $\frac{3}{2}$ ft/sec
• C. $\frac{2}{4}$ ft/sec
• D. $\frac{3}{\sqrt{2}}$ ft/sec

Answer 1

The correct option is B

$\frac{3}{2}$ ft/sec

Finding the rate of approaching the wall:

The ladder makes $30°$ with the wall.

And wall and ground makes $90°$ angle.

So the ladder makes$[180-(90+30\left)\right]=60°$ with the ground.

It is shown that the man is ascending at the rate of $3$

So, the component of this rate along the horizontal is given by:

$\begin{array}{rcl}3\cos \left(60\right)& =& 3\left(\frac{1}{2}\right)\\ & =& \frac{3}{2}feet\backslash seconds\end{array}$

Hence, his rate of approaching the wall is $\frac{\mathbf{3}}{\mathbf{2}}$ feet/seconds, option (B) is correct option.