Question

A man running on a horizontal surface at 3 m/s hids falling rain naturally at 4m/s .find the actual velocity of the rain drops

Answer 1

Answer:

ANSWER

let consider the velocity of rain,

v

r

=a

i

^

+b

j

^

v

m

= velocity of man

v

rm

= velocity of rain with respect to man

Condition (1):

v

m

=8

i

^

v

rm

=0

i

^

+b

j

^

v

r

−

v

m

=b

j

^

a

i

^

+b

j

^

−8

i

^

=b

j

^

(a−8)

i

^

+b

j

^

=b

j

^

a−8=0

a=8

Condition (2):

v

m

=12

i

^

v

rm

=

v

r

−

v

m

v

rm

=(a

j

^

+b

j

^

)−12

i

^

v

rm

=(a−12)

i

^

+b

j

^

Make 30

0

angle to the vertical,

a−12

b

=tan30

0

4−12

b

=

3

1

b=−

3

4

So, velocity of rain with respect to the road is,

v

r

=8

i

^

−

3

4

j

^

It's magnitude, ∣

v

r

∣=

(8)

2

+(−

3

4

)

2

v

r

=8.32m/s

Explanation:

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