Question

rain is falling vertically. to a man walking at 3km per hour it appears to fall at 30 degrees with the vertical. he increases his speed. now it appears to him to fall at 60 degrees with the vertical. what is his new speed?

Answer 1

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

​

Explanation:PLEASE MARK AS BRAINLIEST