A train is moving towards a destroyed bridge. The velocity of the train remains constant at 20 m/s. A person inside the train realizes that they will die unless they run to the back of the train and jump out. If the person is 15 m from the back of the train and the back of the train is 50 m from the break in the track, what velocity must the person run with to make it to the back of the train just as the back of the train goes over the break in the bridge...
a. relative to the train?
b. relative to the ground?
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To calculate the velocity the person must run with, we need to consider the motion of the person relative to both the train and the ground. Let's solve each case individually:
a. Relative to the train:
Since the person is on the train, their velocity relative to the train would be 0 m/s if they are standing still. However, they need to be able to reach the back of the train as it goes over the break in the bridge. To do this, they need to have the same velocity as the train, which is 20 m/s. Therefore, the person must run with a velocity of 20 m/s relative to the train.
b. Relative to the ground:
To calculate the velocity of the person relative to the ground, we need to take into account the velocity of the train. The train is moving at a constant velocity of 20 m/s, and the person wants to reach the back of the train while it goes over the break in the bridge.
Let's assume that the positive direction is towards the break in the track. The velocity of the person relative to the ground would be the sum of their velocity relative to the train and the velocity of the train. So, the person needs to run with a velocity of (20 m/s + 20 m/s) = 40 m/s relative to the ground.
Therefore, the person must run with a velocity of 20 m/s relative to the train and 40 m/s relative to the ground.