A man is walking due east at the rate of of 4kmph and the rain is falling 30° east of vertical with a velocity of 6kmph the velocity of rain relative to the man will be?

1 Answer
Steve J.
Jul 30, 2018

#V_"res" = 5.3 "km"/"hr"#

Explanation:

The vertical component of the rain's velocity is

#V_"rv" = 6 "km"/"hr"*cos30^@ = 5.2 "km"/"hr"#

The horizontal component of the rain's velocity is

#V_"rv" = 6 "km"/"hr"*sin30^@ = 3 "km"/"hr"#

To the man, the vertical component of the falling rain is #5.2 "km"/"hr"#
and the
horizontal component of the falling rain is #(4-3) "km"/"hr" = 1 "km"/"hr"#.

To the man, the velocity of the falling rain is the resultant of those 2 velocity components:

#V_"res" = sqrt(5.2^2 + 1^2) "km"/"hr" = 5.3 "km"/"hr"#

I hope this helps,
Steve

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