For a man walking with certain speed it appears to rain vertically down wards. When he doubles his speed it appears to rain at 30° to the vertical. The angle made by the actual velocity of rain with the vertical is
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Answer:
To man walking a the rate of 3km/h the rain appears to fall vertically
When he increases his speed to
=6km/h it appears to meet him at an angle of 45° with verticl.
Find the velocity the rain.
Solution
Let
i
^
and
j
^
be unit vector in horizontal and vertical respectively
Let, velocity of rain v
r
=a
i
^
+b
j
^
Speed off the rain=
a
2
+b
2
Case 1
When the relative velocity of rain with respect to man is vertical
v
rms
=
v
r
−
v
m
v
m
=3
i
^
v
rms
=(a−3)
i
^
+b
j
^
Since v
rms
is vertical
a+3=0⇒a=3
Case 2
When relative velocity is at 45°
m
=6
i
^
v
rms
=(a−6)
i
^
+b
j
^
=3
i
^
+b
j
^
And since tanθ=
−3
b
tan45°=1
∣b∣=3
Therefore speed=
3
3
+3
2
=3
2
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