Question

Rain is falling with a speed of
4m/s in a direction making an
angle of 30® with vertical
towards south. What should
be the magnitude & direction
of velocity of cyclist to hold his
umbrella exactly vertical, so
that rain does not wet him:
A) 2 m/s towards North
B) 4 m/s towards South
C) 2 m/s towards South
D) 4 m/s towards North
E) Other:​

Answer 1

Given :

The velocity of rain, Vr = 4 m/s.

The angle at which the rain appears to man, θ =0°.

To Find:

We have to find the magnitude and direction of the velocity of the cyclist to hold his umbrella exactly vertical.

Solution:

General equation to find the relative velocity of rain w·r·t man is,

                                      $\[\overrightarrow {{V_{r/m}}} = \overrightarrow {{V_r}} - \overrightarrow {{V_m}} \]$

where,

$\[\overrightarrow {{V_{r/m}}} \]$ → Velocity of rain w·r·t man/ cyclist

$\[\overrightarrow {{V_r}} \]$     → Velocity of rain w·r·t ground

$\[\overrightarrow {{V_m}} \]$    → Velocity of man w·r·t ground

According to the given situation, the rain appears to be falling vertically.      ∴ The horizontal component of  $\[\overrightarrow {{V_{r/m}}} \]$ is zero.

The magnitude of the velocity of the cyclist is given by,

                                      $\[\begin{array}{c}\overrightarrow {{V_m}} = \overrightarrow {{V_r}} \sin \phi \\\\ = 4\sin {30^ \circ }\\\\ = 4 * \frac{1}{2}\\\\ = 2\,{m \mathord{\left/ {\vphantom {m s}} \right. \kern-\nulldelimiterspace} s}\\\therefore \,\overrightarrow {\,\,{V_m}} = 2\,{m \mathord{\left/ {\vphantom {m s}} \right. \kern-\nulldelimiterspace} s}\end{array}\]$

Since the rain is falling towards the south direction, the direction of the velocity of cyclist is also towards south.

Hence, the magnitude and direction of the velocity of the cyclist must be 2 m/s towards the south, so that rain does not wet him.

Option C is correct.

Answer 2

Answer:

The above given asnwer is wrong . Dont rely on it .

The correct answer is 2 m/s (towards north)

Explanation:

In order to hold umbrella, vertical cyclist has to travel towards north such that horizontal component of rain equal to velocity of cyclist.

∴ vM = 4 sin 30° = 2 m/s (towards north)

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