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

$\small{\underline{\sf{\blue{Given:\rightarrow}}}}$

• Velocity of train wrt ground = 12mps
• Velocity of cyclist wrt ground = 17mps
• Both move in the same direction.

$\small{\underline{\sf{\red{To\:Find:\rightarrow}}}}$

• ⇝Velocity of cyclist wrt train.

$\pink{\underline{\sf{\blue{Concept\:used:\rightarrow}}}}$

➡ 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.

$\small{\underline{\sf{\blue{Calculation\:\rightarrow}}}}$

• Velocity of train = V_t
• Velocity of cyclist = V_c
• Velocity of cyclist wrt train = V_ct

⇢$V_{ct}=V_{c}−V_{t}$

⇢$V_{ct}=17−12$

⇢$Vct=5m/s$

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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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Answer 2

$\small\underline\sf\red{Given:}$

Velocity of train wrt ground = 12mps

Velocity of cyclist wrt ground = 17mps

Both move in the same direction.

$\small\underline\sf\red{To\:find\:}$

Velocity of cyclist wrt train.

$\small\underline\sf\red{Method\:Used\:}$

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

$\small\underline\sf\red{VAB\:=VA\:−VB\</p><p>:}$

Where V_A and V_B are the velocities wrt ground.

$\small\underline\sf\red{Calculating:}$

Velocity of train = V_t

Velocity of cyclist = V_c

Velocity of cyclist wrt train = V_ct

${\huge{\boxed{\overline{\mid{\red{Vct=5m/s}}}}}}$