A man standing on a road has to hold his umbrella at 30 degree with the vertical to keep the rain away . He throws the umbrella and starts running at 10km/hr. He finds that the raindrops are hitting his head vertically . What is the speed of rain with respect to ground?
Answers
Answer:
Velocity of the man v
m
running with is 10
i
^
when man run he found that rain falling verticaly hitting his head
Let velocity of rain with respact to man v
r/m
=−v
j
^
velocity of rain v
r
=v
r/m
+v
m
=−v
j
^
kmph+10
i
^
kmph
tan30
0
=
v
10
⇒v=10
3
kmph
we gat v
r
=10
i
^
−10
3
j
^
magnitude we v=
10
2
+(10
3
)
2
=20kmph
Explanation:
When the man is at rest w.r.t. the ground, the rain comes to him at an angle 30o with the vertical. This is the direction of the velocity of raindrops with respect to the ground.
Here Vrg= velocity of rain with respect to the ground.
Vmg= velocity of man with respect to the ground.
and Vmn= velocity of rain with respect to the man.
We have Vrg=Vrm+Vmg........(i)
Taking horizontal components equation (i) gives.
Vrgsin30o=Vmg=10 lm/hr
or Vrg=sin30o10=20 km/hr
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