Answer to Question #92944 in Mechanics | Relativity for Cyrelle Laureano Senorin

Question

A boy is inside a bus moving at 5.0m/s toward the east. He is walking at 1.0 m/s toward the front. What is the velocity of the boy as observed by (a) a passenger sitting inside the bus and (b) another passenger waiting for the bus at a nearby bus stop?

Answer 1

For relative velocities it is necessary to establish:

$V_{P/A}=V_{P/B}+V_{B/A}$

Where:

• Velocity ​​of the particle (child) with respect to A (Observer passenger)

$V_{P/A}$

• Bus velocity (reference B) with respect to A (observer passenger)

$V_{B/A}$

• Particle velocity P (child) with respect to B (buss)

$V_{p/B}$

Now.

Part A

Velocity of the child with respect to the bus:

$V_{P/B}=1.0\frac{m}{s}$

Velocity of the bus with respect to the passenger. (moves at the same velocity as the bus)

$V_{B/A}=0\frac{m}{s}$

Now, evaluating numerically

$V_{P/A}=1.0\frac{m}{s}+0\frac{m}{s}$

The velocity relative to the child on the bus is:

$V_{p/A}=1.0\frac{m}{s}$

Part B

Velocity of the child with respect to the bus.

$V_{P/B}=1.0\frac{m}{s}$

velocity of the bus with respect to the observer.

$V_{B/A}=5.0\frac{m}{s}$

Numerically evaluating

$V_{P/A}=5.0\frac{m}{s}+1.0\frac{m}{s}$

The relative speed of the child with respect to waiting outside the bus is:

$V_{P/A}=6.0\frac{m}{s}$