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Velocity

The speed of an object in a given direction.

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Velocity

Students will learn how analyze and solve problems in two dimensions containing velocity vectors but no acceleration.

Key Equations

vx=vcosθ, where θ is the angle between the velocity vector and the horizontal.

vy=vsinθ, where θ is the angle between the velocity vector and the horizontal.

Δx=vxt

Δy=vyt

Guidance
The only equation you need is that displacement in a certain direction equals the component of velocity in that direction multiplied by the time it takes. You'll use this once for the x-direction and once for the y-direction and solve for what is asked.

Example 1

Question: If a river is flowing north at 2 m/s and you swim straight across (i.e. east) at 1.5 m/s, how far up shore will you be from your starting point once you reach the other side? The river is 9 m wide.

Answer: First solve for the time it takes you to reach the other side. Let's let north be the y-direction and the direction across the river be the x-direction.

Δx=vxt

9m=1.5m/s×t

thus, t=6s

Now, use the time you are in the water to find how far the river has carried you north.

Δy=vyt

Δy=2m/s×6s

Δy=12m

Watch this Explanation

Simulation

Explore More

  1. If a river is flowing south at 4 m/s and you swim straight across (i.e. east) at 2 m/s; admittedly, you're going to drift a bit south. That said, calculate that distance that you drifted south from your starting point. The river is 16 m wide.
  2. If a river is flowing south at 3 m/s and you swim at an angle of 30 degrees north of directly east at 1 m/s, how far did you drift up or down stream from your starting point once you reach the other side? The river is 10 m wide.
  3. If a river is flowing north at 2 m/s and you can swim at 4 m/s, what angle should you swim at such that you arrive directly across the river (i.e. no drift north or south from starting point on other side)? The river is 10 m wide.
  4. If a river is flowing south at 5 m/s and you can swim at 4 m/s maximum, is it possible to arrive directly across? Why or why not?

Answers to Selected Problems

  1. 32m
  2. 28.9m south of starting point
  3. 30 degrees
  4. No, even if you swim directly north the river will still take you south at 1 m/s

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