Question

A ladder is inclined to a wall making and angle of ${30}^0$ with it. A man is ascending the ladder at the rate of $2\text{m/s}$. How fast is he approaching the wall?

• A. $2\text{m/s}$
• B. $1.5\text{m/s}$
• C. $1\text{m/s}$
• D. $0.5\text{m/s}$

Answer 1

Answer: (C)

$1\text{m/s}$

According to the figure, let AC represent the magnitude of velocity vector from point C on ground to point A on the wall, that is AC= 2 m per s and $\angle BAC={30}^o$ degree.

Then, by trigonometry, $sin{30}^o=\frac{BC}{AC}$

where BC is the magnitude of velocity vector from C to wall.

Then $sin{30}^o=\frac{BC}{AC}$

$\Rightarrow \frac{1}{2}=\frac{BC}{2m/s}$

$\Rightarrow BC=1m/s$

Then he approaching the wall