Question

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.

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)