Question

a small ball is moving inside a small tube at a speed of 4 meter per second and the tube itself is moving in the room at a speed of 3 meter per second along a direction perpendicular to it's length. draw the dosgram to show the direction and angle. also find how fast is the ball moving as seen from tha room (physics question for class 11 )

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Answer 1

Given:

A small ball is moving inside a small tube at a speed of 4 meter per second and the tube itself is moving in the room at a speed of 3 meter per second along a direction perpendicular to it's length.

To find:

• Net Velocity of ball and the angle of its motion.

Calculation:

Considering the attached diagram:

Let Velocity of ball be v_{b}:

$\therefore \: \vec{v}_{b} = 4 \hat{i}$

Let Velocity of tube be v_{t}:

$\therefore \: \vec{v}_{t} = 3\hat{j}$

So, net Velocity of ball :

$\therefore \: \vec{v}_{net} = \sqrt{ {(v_{b})}^{2} + {(v_{t})}^{2} }$

$= > \: \vec{v}_{net} = \sqrt{ {(4)}^{2} + {(3)}^{2} }$

$= > \: \vec{v}_{net} = \sqrt{16 + 9}$

$= > \: \vec{v}_{net} = \sqrt{25}$

$= > \: \vec{v}_{net} = 5 \: m {s}^{ - 1}$

Now , let the angle between resultant Velocity and Velocity of ball be $\theta$:

$\therefore \: \cos( \theta) = \dfrac{4}{5}$

$= > \: \theta = {37}^{ \circ}$

Hope It Helps.