For a man walking towards east with a velocity of 5 km/hr rain appears to fall vertically down. When the man begins to walk towards west with a velocity of 3 km/hr the rain appears to fall at an angle of 60° to the vertical. The magnitude of velocity of the rain when the man stops walking is √(139/N). Then N is equal to
Physics · Mixed Chapter
JEE Mains

Question

For a man walking towards east with a velocity of 5 km/hr rain appears to fall vertically down. When the man begins to walk towards west with a velocity of 3 km/hr the rain appears to fall at an angle of 60° to the vertical. The magnitude of velocity of the rain when the man stops walking is √(139/N). Then N is equal to

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Take east positive. Rain appears vertical to a man walking east at 5 km/h, so the horizontal component of rain velocity is vᵣₓ=+5 km/h. Step 2: When the man walks west at −3 km/h, relative horizontal rain speed is 5−(−3)=8 km/h. This relative rain direction makes 60° with vertical, so tan60°=8/|vᵣᵧ|. Step 3: Thus |vᵣᵧ|=8/√3 km/h. Rain speed squared =5²+(8/√3)²=25+64/3=139/3. Step 4: Rain speed=√(139/3) km/h, hence N=3. Answer: 3.