Question

Rain drops are falling with velocity 2i_3j m/s what should be the velocity of man so rain drps hit him with speed 5 m/s

Answer 1

Answer:

$\displaystyle{a=6\hat{i} \ or \ -2\hat{i}}$

Explanation:

$\displaystyle \text{Let the velocity of man is a\hat{i} m/sec}\\\\\displaystyle \text{Now relative velocity of rain with respect man}\\\\\displaystyle{i.e. \ 2\hat{i}-3\hat{j}}\\\\\displaystyle{Applying \ condition}\\\\\displaystyle{5^2=2\hat{i}-a\hat{i}-3\hat{j}}\\\\\displaystyle{5^2=(2-a)\hat{i}-3\hat{j}}\\\\\displaystyle{25=(2-a)^2+9}\\\\\displaystyle{2-a=\pm4}\\\\\displaystyle{a=-2\hat{i} \ or \ 6\hat{i}}$

Thus we get  velocity of man .

Answer 2

Answer :-

The velocity of the man -2i or 6i m/s .

Explanation :-

A rain drop is falling with velocity (2i - 3j) m/s.

___________________[Given]

The velocity of the man will be in horizontal direction .

Let the velocity of the man be ai m/s.

___________________[Assume]

So, the relative velocity of the rain drop w.r. to man will be (2 - a)i - 3j

By the given condition

|(2 - a)i - 3j| = 5

➞ √[(2 - a)² + 3²] = 5

➞ [(2 - a)² + 3²] = 5²

➞ (2 - a)² + 9 = 25

➞ (2 - a)² = 16

➞ (2 - a) = ± 4

➞ a = 2 - 4 Or a = 2 + 4

➞ a = -2 Or a = 6

So,

The velocity of the man is -2i or 6i m/s .

____________________[Answer]