Question

Rain is falling with speed 12 $\sqrt{2}m/s$ at an angle of ${45}^{\circ }$
with a vertical line. A man in a glider going at a speed of u at an angle of ${37}^{\circ }$ with respect to ground. Find the speed of glider so that rain appears to him falling vertically. Consider the motion of glider and raindrops in the same vertical plane.

• A. 15 m/s
• B. 30 m/s
• C. 10 m/s
• D. 25 m/s

Answer 1

Answer: (A)

15 m/s

Convert the velocity vectors into horizontal and vertical components.

So the velocity of rain wrt ground, $v_{RG}=12\sqrt{2}$.

The horizontal component will be $v_{RG}Cos45$, i.e. $12$ in positive $x$ direction.

Vertical component will also be $12m/s$ in negative $y$ direction.
Now,

Velocity of man with respect to ground, $v$.

Horizontal component of $v$ will be $\frac{4v}{5}$ in negative $x$ direction, vertical component will be $\frac{3v}{5}$ in negative $x$ direction.

By equation

$v_{RM}+v_{MG}=vRG$
For rain to appear falling only in vertical plane to the man, velocity of rain in the horizontal plane must be zero to the man,i.e. $v_{RM}=0$ in horizontal plane.

Now consider equation * for horizontal motion,

$0+v_{MG,X}=v_{RG,X}$

$v_{MG,X}=\frac{4v}{5}$

​So, $\frac{4v}{5}=12$

Hence, $v=15m/s$.