What happens to the speed and direction of the passenger's velocity relative to the water if the speed of the boat doubles?
To understand what happens to the speed and direction of the passenger's velocity relative to the water when the speed of the boat doubles, we need to break it down step by step.
First, let's establish a few things:
1. The passenger's velocity is with respect to the water, which means it is measured from the standpoint of an observer standing on the water.
2. The boat's velocity is also with respect to the water, as it is moving on the water's surface.
3. The boat is carrying the passenger.
Now, let's consider the scenario where the speed of the boat doubles:
1. Doubling the speed of the boat means the magnitude of the boat's velocity relative to the water is now twice what it was before. So, if the boat was initially moving at x units of speed, it will now move at 2x units of speed.
2. Since the passenger is on the boat, their velocity relative to the water is determined by adding their own velocity (relative to the boat) to the boat's velocity (relative to the water). This is known as the vector addition of velocities.
3. If the passenger is stationary relative to the boat (not moving), their velocity relative to the water will be the same as the boat's velocity. So, when the boat's speed doubles, the passenger's velocity will also double.
4. However, the direction of the passenger's velocity relative to the water remains unchanged, assuming the passenger stays stationary on the boat. The passenger's velocity vector would still be in the same direction as the boat's velocity vector.
In summary, if the speed of the boat doubles, the speed of the passenger's velocity relative to the water will also double, while the direction of the passenger's velocity relative to the water will remain unchanged.