A person walks at a speed of 2 m/s toward the front of a train moving at 20 m/s in the same direction. Calculate the person's speed and direction relative to the ground.
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To calculate the person's speed and direction relative to the ground, we need to find the vector sum of the person's velocity relative to the train and the train's velocity relative to the ground.
The person's velocity relative to the train is simply 2 m/s towards the front of the train.
The train's velocity relative to the ground is 20 m/s in the same direction.
To find the person's velocity relative to the ground, we add the two vectors:
Person's velocity relative to the ground = Person's velocity relative to the train + Train's velocity relative to the ground.
In terms of magnitude, the person's velocity relative to the ground is given by:
|Person's velocity relative to the ground| = sqrt((2^2) + (20^2))
|Person's velocity relative to the ground| = sqrt(4 + 400) = sqrt(404) ≈ 20.1 m/s
The direction of the person's velocity relative to the ground can be determined by finding the angle between their velocity vector and the positive x-axis.
The direction θ is given by:
θ = tan^(-1)((20)/(2)) = tan^(-1)(10) ≈ 84.3 degrees
Therefore, the person's speed relative to the ground is approximately 20.1 m/s, and their direction relative to the ground is approximately 84.3 degrees.
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