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when a man moves down an inclined plane with const. speed 5m/swhich make an angle 37 with the horizontal, he finds rain falling vertically downwards. when he moves up the same inclined plane with same speed , he finds the rain making an tan^-1(7/8)with horizontal then speed of rain is?
Dear sneha ,
Please see the figure to find the axis assumed.
let the x- component of rain be x and that of y be y . Now , apply the concepts of relative velocity , subtract the x component of man's velocity from rain 's xcomponent and same for y component of rain.
now , man's x component = 5 *cos37 = 4 m/s , man's y component = 5 sin37 = - 3 m/s
so , velocity of rain relative to man : x component = x -(4 ) = (x - 4) m/s ; y component = (y +3) m/s
as the velocity seems vertical horizontal component must be zero , so x - 4 =0 , x = 4 m/s
second case , man's x component = - 5 *cos37 = -4 m/s , man's y component = 5 sin37 = 3 m/s
so , velocity of rain relative to man : x component = x -( -4 ) = (x + 4) m/s ; y component = (y -3) m/s
as angle from the horizontal is tan ^-1 (7/8) , ; 7/8 = -( y- 3) / x +4
7/8 = 3-y /8 , therefore , y = -4 m/s , i.e 4m/s downwards .
so velocity of rain is (42 +42 )1/2 = 5.65 m/s 45deg to the vertical.
GOOD LUCK !!!
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