0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

A train of length l=350m starts moving rectilinearly with constant acceleration ω=3.0102m/s2; t=30s after the start the locomotive headlight is switched on (event 1), and τ=60s after that event the tail signal light is switched on (event 2) . At what constant velocity V (in m/s) relative to the Earth must a certain reference frame K move for the two events to occur in it at the same point? (round off your answer to the nearest integer)

Solution
Verified by Toppr

In the reference frame fixed to the train, the distance between the two events is obviously equal to l. Suppose the train starts moving at time t=0 in the positive x direction and take the origin (x=0) at the head-light of the train at t=0. Then the coordinate of first event in the earth's frame is
x1=12wt2
and similarly the coordinate of the second event is
x2=12w(t+τ)2l
The distance between the two events is obviously,
x1x2=lwτ(t+τ2)=0.242km
in the reference frame fixed on the earth.
For the two events to occur at the same point in the reference frame K, moving with constant velocity V relative to the earth, the distance travelled by the frame in the time interval T must be equal to the above distance.
Thus Vτ=lwτ(t+τ2)
So, V=1τwτ(t+τ2)=4.03m/s
The frame K must clearly be moving in a direction opposite to the train so that if (for example) the origin of the frame coincides with the point x1 on the earth at time t, it coincides with the point x2 at time t+τ.

Was this answer helpful?
0
Similar Questions
Q1
A train of length l=350m starts moving rectilinearly with constant acceleration ω=3.0102m/s2; t=30s after the start the locomotive headlight is switched on (event 1), and τ=60s after that event the tail signal light is switched on (event 2) . At what constant velocity V (in m/s) relative to the Earth must a certain reference frame K move for the two events to occur in it at the same point? (round off your answer to the nearest integer)
View Solution
Q2
Two events A and B occur at places separated by 106 km, B occurring 5 s after A. (a) Find the velocity of a frame in which these events occur at the same place. (b) What is the time interval between the events in this frame?
View Solution
Q3

The velocity of a body, starting at rest and freely falling towards Earth, after one second is ___ m/s. (Round your answer to the nearest integer)

View Solution
Q4
A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m=0.4kg is at rest on this surface. An impulse of 1.0N s is applied to the block at time to t=0 so that it starts moving along the x-axis with a velocity v(t)=v0etτ, where v0 is a constant and τ=4s. The displacement of the block, in metres, at t=τ is ___________.
[Take e1=0.37]
Round off your answer to nearest integer.
View Solution
Q5
The velocity of a freely falling body, starting at rest and after one second is ___ m/s. (Round your answer to the nearest integer)
View Solution