Falling From a Boat: Relative Velocity Explained

• istock1
In summary, two kayakers got into an argument about the relative velocity of a kayak and a person sitting in it in a constant velocity current. The question was whether they would separate if the person fell out of the kayak. The correct answer is that they will not separate as they are both moving with the same constant velocity of the current. However, in practice, they may drift apart due to the initial push of the person falling out and the kayak being lightweight.

istock1

All,

I am an avid kayaker, and recently got into an argument with another kayaking friend of mine over (what I think is) an issue of relative velocity. The question was this:

A person is sitting in a kayak and that kayak is in a constant velocity current (say, 3 knots), but the kayak is not moving relative to the water it is in. If he falls out of the kayak, at what speed will the person and boat separate?

My argument was that they will not separate; they will both continue to move at 3 knots with the current, but will not move relative to the water. Can anyone help settle this?

Thanks!

Ideally, you are correct. I say "ideally," since obviously when you fall into the water, you will probably have some acceleration in some direction, and so will start to move in that direction. However, the answer (I think you want) is that no, the boat and person will not separate, since both the boat and the person are moving with the same constant velocity of the water.

Falling out of a kayak, you'll probably push it away with your feet. Once you are in the water, it will drift with the wind and you won't...

russ_watters said:
Falling out of a kayak, you'll probably push it away with your feet. Once you are in the water, it will drift with the wind and you won't...

Russ,

Of course you are right, and I should have included that we were holding windspeed at zero.

Thanks!

you mean, holding windspeed at 3 knots?

Heh - right. Assuming the wind is moving the same speed as the current, there is no motion between you and the kayak.

Assuming wind is discounted:

There's going to be no "residual" velocity. Both you and the kayak will virtually instantly achieve the same velocity as the current.

Now, in practice, you and the kayak will likely drift apart from the initial push of you falling in. This distance will be in whatever direction you fall in, independent of the current. And the kayak is so light that this could become a significant distance.

1. What is relative velocity?

Relative velocity is the measure of the velocity of an object in relation to another object. It takes into account the motion of both objects and calculates the difference between their velocities.

2. How does relative velocity apply to falling from a boat?

When a person falls from a moving boat, their velocity is affected by both the boat's velocity and their own. The relative velocity between the person and the boat will determine their trajectory and where they will land in the water.

3. How does the direction of the boat's velocity affect a person falling from it?

If the boat is moving in the same direction as the person falling, their relative velocity will be lower and they will land closer to the boat. However, if the boat is moving in the opposite direction, their relative velocity will be higher and they will land further away from the boat.

4. Can relative velocity be used to determine the speed of a boat?

No, relative velocity only considers the difference in velocity between two objects. To determine the speed of a boat, the velocity of the boat itself must be measured.

5. How does the mass of the objects affect relative velocity?

The mass of the objects does not affect relative velocity. It is solely determined by the velocities of the objects and their direction of motion.