Question

A train is travelling East at a speed of 12 m/s relative to an observer standing on the ground. A cyclist is riding her cycle on the train and a ground observer finds her velocity to be 17 m/s towards the East. How fast is she moving with respect to another passenger on the train?

Answer 1

Given :

▪ Velocity of train wrt ground = 12mps

▪ Velocity of cyclist wrt ground = 17mps

▪ Both move in the same direction.

To Find :

▪ Velocity of cyclist wrt train.

Concept :

➡ This question is completely based on the concept of relative motion.

➡ When the objects A and B move in the same directions, Relative velocity of object A wrt B is given by

$\bigstar\:\underline{\boxed{\bf{\pink{V_{AB}=V_A-V_B}}}}$

✒ Where V_A and V_B are the velocities wrt ground.

Calculation :

⏭ Velocity of train = V_t

⏭ Velocity of cyclist = V_c

⏭ Velocity of cyclist wrt train = V_ct

$:\implies\sf\:V_{ct}=V_c-V_t\\ \\ :\implies\sf\:V_{ct}=17-12\\ \\ :\implies\underline{\boxed{\bf{\gray{V_{ct}=5mps}}}}\:\red{\bigstar}$

Answer 2

Aɴꜱᴡᴇʀ

☞ Your answer is 5 m/s

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Gɪᴠᴇɴ

➢ A train is travelling East at a speed of 12 m/s as per an observer on ground

➢ A cyclists is riding East on the train whose velocity is 17 m/s as per a ground observer

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Tᴏ ꜰɪɴᴅ

✭ Speed of the cyclists with respect to a passenger on the train?

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Sᴛᴇᴘꜱ

$\large\underline{\boxed{ \sf{\green{V_{AB}=V_A-V_B}}}}$

$\dashrightarrow\sf V_{ct}=V_c-V_t\\ \\ \dashrightarrow\sf V_{ct}=17-12\\ \\ \dashrightarrow{ \sf{\pink{V_{ct}=5m/s}}}$

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Additional information :-

✭ The motion of a body with respect to another body is called relative motion.

✭ Ex: A bus moving with some speed according to a person who is outside from the bus .The persons are in motion who is in the bus.This is called relative motion from the bus.

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