Relative Velocity SPH4U

Inertial Reference Frames The equations of motion will be valid in any reference frame that is at rest (A) or moving uniformly at a constant velocity (C):

Inertial Reference Frames These reference frames are said to be inertial. inertial non-inertial

Relative Motion All motion in inertial reference frames is therefore relative:

Relative Motion All motion in inertial reference frames is therefore relative:

Adding Vectors To transfer between reference frames, we add the velocity vectors:

Example 1 A passenger is walking at 2.0 m/s [E] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer?

Example 1 A passenger is walking at 2.0 m/s [E] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer?

Example 1 A passenger is walking at 2.0 m/s [E] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer?

Example 2 A passenger is walking at 2.0 m/s [N] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer?

Example 2 A passenger is walking at 2.0 m/s [N] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer? 9.0 m/s 2.0 m/s

Example 2 A passenger is walking at 2.0 m/s [N] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer? 9.0 m/s 2.0 m/s

Example 2 A passenger is walking at 2.0 m/s [N] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer? 9.0 m/s 2.0 m/s

Example 2 A passenger is walking at 2.0 m/s [N] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer? 9.0 m/s 2.0 m/s

Example 2 A passenger is walking at 2.0 m/s [N] on a train travelling at 9.0 m/s [E]. What is his velocity relative to a ground-based observer? 9.0 m/s 2.0 m/s

Example 3 A canoeist paddling at 4.5 m/s is crossing a river flowing at 3.2 m/s [E]. At what angle should she aim the canoe to land due North of her starting position?

Example 3 A canoeist paddling at 4.5 m/s is crossing a river flowing at 3.2 m/s [E]. At what angle should she aim the canoe to land due North of her starting position? velocity of the water relative to the shore velocity of the canoe relative to the water velocity of the canoe relative to the shore

Example 3

She should paddle 45 o W of N.

Components When given vectors at angles, break them down into their horizontal and vertical components and add the components.

Components When given vectors at angles, break them down into their horizontal and vertical components and add the components.

Alternately or use the Sine Law and Cosine Law (for an example, refer to p. 55, Sample Problem 2)

More Practice Textbook Questions: p. 56 #2 p. 57 #3, 4 A real-world application of relative motion problem-solving (from thinkgeek.com):

Addendum Please note that a rotating reference frame is never inertial. Even if it is rotating at constant speed, the direction of the velocity vectors is always changing.

More Later We will be studying rotating reference frames in more detail later.