Lets analyze the observation of rain fall
. by man on ground. Say if a man holding an
umbrella and rain is falling vertically. Certainly
this umbrella will be able to save man from
the rain fall. But what happened if the man
starts walking with the velocity v m. Say
man starts walking we can easily calculate
how the man will feel , the rain fall is coming
. so if we calculate the velocity of, rain
drops. With respect to man. Is velocity of
rain drops with respect to man can be given
as v r minus , v m. Now if we just calculate
the direction of , this rain fall with respect
to man , so we can simply state rain is falling
in vertically downward direction say this
v r vector, man is moving toward right with
the velocity v m vector so minus v m vector
would be this. So resultant will be in this
direction it is a velocity of rain drops with
respect to, man. That means as man will observe
the rain fall man will fell that rain is falling
at an angle theta from the vertical . where
tan theta can be given as , the ratio of magnitude
of v m and v r. This the angle at which the
rain appears to be coming, with respect to
man. So if while walking he is holding the
umbrella in vertical direction , and rain
drops are hitting to the man in the direction
theta with the vertical , certainly the man
is going to be wet. So to save, himself from
the rainfall he has to hold the umbrella , in
such a way , that it’ll be able to , stop
the rain drops with respect to man hitting
to him . like say if this is the man , so
he has to hold the umbrella , in this direction
, where we can say , rain drops, appear to
be coming towards the man . this is a velocity
of rain with respect to man , at an angle
theta with the vertical with which the rain
appear to be falling . so even, there is no
umbrella over head, still he’ll not get
wet because , the rain drops which is coming,
towards him , it’ll be saved by the umbrella
, and it’ll be going away. The rain drops
which is falling on to it when it’ll fall
before that he’ll be able to move forward
, and umbrella will be able to save the rain
drops, which are going to hit the man in vertical
direction . so this the way how he has to
hold the umbrella to save himself , actually
umbrella will be able to save the man if it
is in direction, which is opposite to the
velocity of rain drops , with respect to ,man.
In this example we are given that a man is
standing on ground with an umbrella hat as
shown. Suddenly rain fall starts at a speed
20 meters per second at an angle 30 degree
with the vertical . we are required to find
the speed and direction in which man should
start running so as to save himself. In this
situation, we can see that, the man is wearing
an umbrella hat. This umbrella hat is very
small in size and it can save man only when
rain is, falling vertically . when rain fall
starts in vertical direction . but here rain
is falling in the direction at an angle theta
with the vertical , so obviously this umbrella
hat will not be able to save him. In this
case the man should start running, in such
a way that velocity of rain, with respect
to this man should become vertically down
, than this umbrella will be able to save
him. Say here you can simply write down in
the solution , we can write , to save. The
man. He should run. Such that. Velocity of
rain with respect to man , becomes vertically
down. If it becomes vertically down, this
umbrella will be able to, save him. So here
we know velocity of rain with respect to man
we can write as v r minus, v m. We are required
to find the value of v m. So here v m can
be given as, v r minus v r m. So in this situation
we can see that v r in this direction , this
the velocity v r , at an angle, theta i.e.30
degree with the vertical and the value of
v r is also given. If v r m is in vertically
downward direction , if rain with respect
to man is in vertically downward direction,
then minus v r m will be in vertically upward
direction , so the resultant will be toward
left, which is velocity of man. So man has
to run toward left with the velocity v m , and
this v m, magnitude can be directly given
by this triangle, as v m =, v r sine theta
, i.e. = 20 sine 30 degree or it is 10 meters
per second . this is the answer to this problem
. so man has to run toward left, with the
velocity 10 meters per second , due to this,
it’ll appear to man that rain is falling
vertically , so this umbrella hat will be
able to save the man . or we can say or we
can solve this problem, orally or directly
also. like if rain is falling at a velocity
v r. Its vertical component can be written
as v r coz theta and its horizontal component
with which the rain is, travelling , or rain
drops are travelling in horizontal direction
as v r sine theta. So, if we talk about vertical
component of rain drops umbrella is able to
save the man. For horizontal component man
will not be saved , so he has to run in such
a way that horizontal speed of rain, appear
to man will be= 0. So we can directly say
the man has to run toward left with the velocity
v r sine theta, so that the relative velocity
of rain drops with respect to man in horizontal
, direction become 0. This the way how you
can directly archive the result, or this is
the systematic way to approach the result
.
