Peoples Physics Concepts

http://www.ck12.org Chapter 3. Two-Dimensional and Projectile Motion

3.2 Velocity

• Analyze and solve problems in two dimensions containing velocity vectors but no acceleration.

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

Key Equations

vx=vcosθ, whereθis the angle between the velocity vector and the horizontal.

vy=vsinθ, whereθis the angle between the velocity vector and the horizontal.

∆x=vxt

∆y=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.

∆x=vxt

9 m= 1. 5 m/s×t

thus,t= 6 s

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

∆y=vyt

∆y= 2 m/s× 6 s

∆y= 12 m

Watch this Explanation