Question

The rain appears to fall vertically with a speed of 3 m/s relative to a man standing on ground. Find the velocity of rain relative to the man when he moves towards east with a speed of 2 m/s (Take XY plane on ground)
1.-2 i^ +3k^
2.2i^-3k^
3.2i^-3j^
4.-2i^+3j^

Answer 1

Given:

The rain appears to fall vertically with a speed of 3 m/s relative to a man standing on ground.

To find:

Velocity of rain relative to the person , when the man starts to walk towards east with the speed of 2m/s.

Calculation:

First refer to the attached diagram to understand the Velocity vectors of rain and man ;

Let Velocity of man be $\vec{v_{m}}$ and that of rain be $\vec{v_{r}}$.

Velocity of rain relative to man will be vector subtraction between Velocity vector of rain and Velocity vector of man.

$\sf{ \therefore \: \vec{v}_{r \rightarrow m} = \vec{v_{r}} - \vec{v_{m}}}$

$\sf{ \implies \: \vec{v}_{r \rightarrow m} = \{ 3( - \hat{j}) \} - \{ + 2( \hat{i}) \}}$

$\sf{ \implies \: \vec{v}_{r \rightarrow m} = - 3 \hat{j} - 2 \hat{i}}$

So, final answer is:

$\boxed{ \large{ \red{ \rm{ \: \vec{v}_{r \rightarrow m} = - 3 \hat{j} - 2 \hat{i}}}}}$