Question

A man is walking on a horizontal road at velocity
of 5 km/h and the rain appears to be falling
vertically at 5 km/h to him. The magnitude of
velocity of rain with respect to the ground is
[NCERT Pg. 76]
(1) 5 km/h
(2) 52 km/h
(3) 10 km/h
(4) 4 km/h​

Answer 1

A man is walking on a horizontal road at velocity of 5 km/h and the rain appears to be falling vertically at 5 km/h to him. The magnitude of velocity of rain with respect to the ground is

(1) 5 km/h

(2) 5√2 km/h

(3) 10 km/h

(4) 4 km/h

Answer: The magnitude of the velocity of rain with respect to the ground is equal to 5√2 km/h. The correct option is (2) 5√2 km/h.

Given:

The man is walking on a horizontal road at a velocity of 5 km/h.

The rain appears to man to be falling vertically at a velocity of 5 km/h.

To Find:

The magnitude of the velocity of rain with respect to the ground.

Solution:

→ Let the velocity of the rain with respect to the ground be $V_{RG}$

→ If the velocity of object A with respect to the ground is $V_{AG}$ and the velocity of an object B with respect to the ground is $V_{BG}$, then the relative velocity of B with respect to A is given by:

           $\therefore Velocity\:of\:B\:with\:respect\:to\:A\:(V_{BA} ) = V_{BG} -V_{AG}$

→ We will assume the direction along the horizontal road and in the direction of motion of the man to be positive x-axis.

→ We will assume the upward direction, perpendicular to the horizontal road to be the positive y-axis.

∴ The velocity of the man with respect to the ground ($V_{MG}$) = (5)${\boldsymbol{\hat{\textbf{\i}}}}$

∴ The velocity of the rain with respect to the man ($V_{RM}$) = $\:{\boldsymbol{-(5)\hat{\textbf{\j}}}}$

→ The velocity of the rain with respect to the man that is $V_{RM}$ would be given by:

      $\therefore Velocity\:of\:Rain\:with\:respect\:to\:Man\:(V_{RM} ) = V_{RG} -V_{MG}$

                                    $\therefore V_{RM} = V_{RG} -V_{MG}\\\\\therefore V_{RG} =V_{RM} +V_{MG}\\\\\:{\boldsymbol{\therefore V_{RG} =-(5)\hat{\textbf{\j}}}} +\:{\boldsymbol{(5)\hat{\textbf{\i}}}}$

→ Therefore the velocity of the rain with respect to the ground comes out to be:   ${\boldsymbol{V_{RG} =\:-(5)\hat{\textbf{\j}} +(5)\hat{\textbf{\i}}}}$

→ Therefore the magnitude of the velocity of rain with respect to the ground is :

                                    $\therefore {V_{RG} }=\sqrt{5^{2} +5^{2} } \\\\\therefore {V_{RG} }=\sqrt{50}\\\\\therefore {V_{RG} }=5\sqrt{2} \:km/h$

Therefore the magnitude of the velocity of rain with respect to the ground is equal to 5√2 km/h. Hence, the correct option is (2) 5√2 km/h.

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Answer 2

A man is walking along a horizontal road at a speed of 5 km/h and the rain appears to fall on him vertically at a speed of 5 km/h. The magnitude of the rain velocity relative to the ground is

• (1) 5 km/h
• (2) 5√2 km/h
• (3) 10 km/h
• (4) 4 km/h

Answer: The magnitude of the speed of rain relative to the ground is equal to 5√2 km/h. The correct choice is (2) 5√2 km/h.

With regard to it:

• A man walks along a horizontal road at a speed of 5 km/h.
• To a person, the rain appears to fall vertically at a speed of 5 km/h.

Find:

The magnitude of the rain velocity relative to the ground be.

Solution:

Let the velocity of the rain relative to the ground be $V_{RG}$.

If the velocity of object A relative to the ground is $V_{AG}$ and the velocity of object B relative to the ground is $V_{BG}$ , then the relative velocity of B relative to A is given by:

The velocity of B with respect to A$(V_{BA} )$=$V_{BG} -V_{AG}$

We will assume the direction along the horizontal path and in the direction of human movement as the positive x-axis.

With the positive y-axis, we will assume the upward direction, perpendicular to the horizontal road.

∴ Speed ​​of man relative to ground ($V_{MG}$) = (5)î

∴ Speed ​​of rain relative to man ($V_{RM}$) =-5j

The speed of the rain relative to the person is $V_{RM}$ given by:

The velocity of rain with respect to man=

     $(V_{RM})=V_{RG}-V_{MG}\\Hence,(V_{RM})=V_{RG}-V_{MG}\\V_{RG}=V_{RM}+V_{MG}\\Hence,V_{RG}=-5j+5i$                  

→ The speed of the rain relative to the ground is, therefore:$V_{RG}=-5j+5i$

→ The magnitude of the rain velocity relative to the ground is, therefore:

$V_{RG}=\sqrt{5^2+5^2} \\V_{RG}=\sqrt{50}\\ V_{RG}=5\sqrt{2}km/h$

Therefore, the magnitude of the velocity of the rain relative to the ground is equal to 5√2 km/h. So the correct option is (2) 5√2 km/h.

Learn more here:

https://brainly.in/question/11504533

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