Two passenger trains are passing each other on adjacent tracks. Train A is moving east with a speed of 35.5 m/s, and train B is traveling west with a speed of 33.4 m/s. (a) What is the velocity (taking due east to be the positive direction) of train A as seen by the passengers in train B? (b) What is the velocity of train B as seen by the passengers in train A?
Amanda/ar/JJ -- please use the same name for your posts.
They are moving in opposite directions
35+33.4=68.4 east and 68.4 west.
To determine the velocity of one train as seen by the passengers in the other train, we need to consider their relative velocities.
(a) Velocity of Train A as seen by the passengers in Train B:
The velocity of Train A relative to Train B is given by the difference in their speeds. Since Train A is moving east and Train B is moving west, we subtract their speeds:
Relative velocity = Velocity of Train A - Velocity of Train B = 35.5 m/s - (-33.4 m/s)
To simplify the calculation, we use the rule that subtracting a negative is the same as adding a positive value:
Relative velocity = 35.5 m/s + 33.4 m/s
Calculating the sum:
Relative velocity = 68.9 m/s (eastward)
Therefore, the velocity of Train A as seen by the passengers in Train B is 68.9 m/s to the east.
(b) Velocity of Train B as seen by the passengers in Train A:
Similarly, the velocity of Train B relative to Train A is given by the difference in their speeds:
Relative velocity = Velocity of Train B - Velocity of Train A = 33.4 m/s - 35.5 m/s
Again, we can simplify this by subtracting a negative:
Relative velocity = 33.4 m/s - (-35.5 m/s) = 33.4 m/s + 35.5 m/s
Calculating the sum:
Relative velocity = 68.9 m/s (westward)
Thus, the velocity of Train B as seen by the passengers in Train A is 68.9 m/s to the west.
To answer these questions, we will use the concept of relative velocity. Relative velocity refers to the velocity of one object as observed or measured by another moving object.
(a) To find the velocity of train A as seen by the passengers in train B:
The velocity of train A as seen by the passengers in train B will be equal to the vector difference between the velocity of train A and the velocity of train B.
Given:
Velocity of train A (VA) = 35.5 m/s (east)
Velocity of train B (VB) = 33.4 m/s (west)
To find the relative velocity, we need to subtract the velocity of train B from the velocity of train A because they are moving in opposite directions:
Relative velocity of A as seen by B (V_rel AB) = VA - VB
V_rel AB = 35.5 m/s - (-33.4 m/s) [Note: The velocity of train B is in the opposite direction, so we take its negative value.]
V_rel AB = 35.5 m/s + 33.4 m/s
V_rel AB = 68.9 m/s (eastwards)
Therefore, the velocity of train A as seen by the passengers in train B is 68.9 m/s (eastwards).
(b) Similarly, to find the velocity of train B as seen by the passengers in train A:
We need to find the relative velocity of train B with respect to train A.
Relative velocity of B as seen by A (V_rel BA) = VB - VA
V_rel BA = 33.4 m/s - 35.5 m/s
V_rel BA = -2.1 m/s (westwards)
Therefore, the velocity of train B as seen by the passengers in train A is 2.1 m/s (westwards).
Note: The negative sign indicates that train B is moving in the opposite direction to train A.