You are riding the TGV. Europe's fastest train, which is traveling. velocity of 540 km/h North. You just realize that you left your favorite book at the back of the train with your luggage. You walk towards the back at a speed of speed of 3 km / h South. What is your resultant velocity?
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Answer:
The resultant velocity is the vector sum of the velocities of the train and the person walking towards the back.
Since the train is moving to the North at 540 km/h, its velocity vector is:
v_train = +540 km/h (North)
And since the person is walking towards the back at 3 km/h, their velocity vector is:
v_person = -3 km/h (South)
To find the resultant velocity, we add the two vectors:
v_resultant = v_train + v_person
Since these two vectors are in opposite directions (North and South), we simply subtract their magnitudes:
|v_train| = 540 km/h
|v_person| = 3 km/h
v_resultant = 540 km/h - 3 km/h = 537 km/h (North)
Therefore, the resultant velocity of the person walking towards the back of the train is 537 km/h North.