Question

rain is falling vertically with the speed of 30m s-1 A women rides a bicycle with a speed of 10 m s-1 in North to south direction . what is the direction in which she should hold her umbrella?​

Answer 1

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18° towards south

${\huge{\boxed{\mathcal{\red{Explanation}}}}}$

It is given that :-

• Velocity of women = vw = 10m/s
• Velocity of rain = vr = 30m/s
• Rain is falling vertically.
• Women is travelling North to South

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Coming to question :-

Women has a umbrella. If women wants to get protected from rain the she should incline her umbrella in direction of Relative Velocity of rain with respect to woman. If she does this she would be protected from rain.

Now relative velocity of rain with respect to women is :-

v = vr + (-vw)

v = 30 + (-10)

$v = 20m \div s$

Now, since rain is vertical and women is travelling horizontal, then graphically we can say

There direction are in ratio Perpendicular / Base.

$\frac{p}{b} = tan \: a$

Now for this the tan =

$\frac{10}{30} = \frac{1}{3}$

Now, tan A = 1/3

A is nearly 18°

Thus we can say that women should hold her umbrella at angle nearly 18° towards South.

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Answer 2

Answer:

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Explanation:

The described situation is shown in the given figure.

Here, v

c

= Velocity of the cyclist

v

r

= Velocity of falling rain

In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the woman.

tanθ=v

c

/v

r

=10/30

θ=18

o

Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18 with the vertical.