Question

A person is running up the inclined plane with speed 4/√3 m/s and rain appers him as falling vertically. What may be velocity of rain? (θ=30)​

Answer 1

Answer:

Write the velocity of man in terms of components

$v_{m}= \frac{4}{ \sqrt{3} } \cos(30) \: {i} + \frac{4}{ \sqrt{3} } \sin(30) \: j \\ \\ = 2 \: i + \frac{2}{ \sqrt{3} } \: j$

Now let velocity of rain is

$v_{r} = v_{x}i + v_{y}j$

Now velocity of rain with respect to man

$= v_{rm} \\ = v_{r} - v_{m} \\ \\ =( v_{ x } - 2)i + (v_{y} - \frac{2}{ \sqrt{3} } )j$

Since rain appears falling vertically so x component of this velocity will be zero . So

$v_{x} - 2 = 0 \\ \\ v_{x} = 2$

So in x direction velocity of rain is 2 i .

Option 2