Question

A man walking west at a speed of 3 km/hr , Raindrops fall vertically with a speed of 3root 3km/hr , Find the velocity of raindrops, with respect to the man , In which direction, the man should hold the umbrella to protect himself from rain


please write your answer mathematically by using formula​

Answer 1

Explanation:

let velocity of rain,vr =ai +bj

Answer 2

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 rrm = 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

This is the correct answer

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