Question

To a man walking at 2kmph on a
horizontal road, rain appears as
falling vertically downwards.
When he doubles his speed, it
appears to fall at 30" with vertical
Actual velocity of rain is
1) 2kmph. 30" with vertical
2) 2kmph. 60" with vertical
3) 4kmph. 30" with vertical
4) 4kmph. 60" with vertical​

Answer 1

Answer:

2√2 km/hr

45° Downwards west

Explanation:

To a man walking due east at the rate of 2km/hr, rain appears to fall vertically. When he increases his speed to 4km/hr ,it appears to meet him at an angle of 45 degree . Find the real direction and speed of rain.

Let say velocity of rain = ai - bj ( - is taken as rain is falling down wards)

Velocity of rain relative to man

Vr - Vm

Vm = 2i

(a - 2)i - bj

Velocity of rain relative to man is vertically so i = 0

=> a - 2 = 0 => a = 2

Vr = 2i - bj

Vr - Vm

Vm = 4i

(a - 4)i - bj = (2 - 4)i - bj = -2i - bj

Angle = 45° => Tan45° = -b/-2 => 1 = -b/-2 => b = 2

Vr = 2 i - 2j

Speed of Rain = √2² + (-2)² = 2√2 km/hr

Direction of rain = -45° ( 45° Downwards west)