For this case we can write each one of the vectors in the following way:
This means that the x-axis is defined as positive towards the west.
Then, the resulting vector is:
Answer:
Displacement vectors of 10 m west and 14 m west make a resultant vector that is 24 m west
Given that,
Distance =30 m
speed = 0.5c
(A). We need to find the bell and siren simultaneous events for a passenger seated in the car
According to given data
The distance travelled by the light to reach either side of the rocket train car is same.
So, The two events are simultaneous and the bell and siren are the simultaneous events for a passenger seated in the car.
(B). We need to calculate time interval between the events
Using formula of time dilation
.....(I)
Where, = proper time
= time interval between the events
The time interval between the events measured in a reference frame
The proper time in this case is
For the second interval,
Put the value of in the equation (I)
Put the value in the equation
Negative sign shows the siren rings before the bell ring.
Hence, (A). Yes, the bell and siren are simultaneous events.
(B). The siren sounds before the bell rings.