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What do we mean by relative motion?

- Δx, v, a… have all been defined with reference to some “point” or coordinate system
- reference frame used so far -> x, y with x=0, y=0 as a reference point
- what if one reference frame is moving and another one is stationary?
- what if both reference frames are moving but with different speed? direction?
- Example: sitting in a parked car and the one next to you begins to move – what is your first sensation? you moving? the other car?

The inner subscripts must match

The outer subscripts on the right

must be the same as those of the

resultant vector

Relative position in one dimension

L=Lambourghini

V=Ventura

P=person

The subscript rule

Relative velocities in one dimension

Important: The equations for relative position and velocity are in VECTOR form. Remember to assign appropriate signs – or + to EACH vector depending on the choice of coordinate system!

Relative velocities in 1D: person walking on a moving train

Velocity of person relative to train

Velocity of train relative to ground

What is the velocity of the person relative to the ground?

The subscript rule:

- the inner subscripts must match

- the outer subscripts on the right must be the same as the resultant vector

Relative motion in 1D: problem solving

- Given:
- VBW = 5 m/s
- VWS = 2 m/s
- Find:
- VBS = ?

A boat travels along a river with velocity of 5 m/s with res-pect to the water. The river flows with velocity of 2 m/s with respect to the shore.

Q. What is the velocity of the boat with respect to the shore when traveling along and opposite to the river flow?

Case 1: boat moving down the river

Case 2: boat moving up the river

shore

Relative motion in 2D: problem solving

- Given:
- VBW = 5 m/s
- VWS = 2 m/s
- Find:
- VBS = ?

A motor boat has to cross a river with velocity of 5 m/s relative to the water. The river flows with 2 m/s relative to the shore.

Q. In what direction should the captain orient the boat, so that its trajectory is perpendicular to the shores?

Consider the triangle ABC and find angle θ

Substitute the angle θ in eq. (1) and find VBS

Relative motion in 2D: problem solving

N

E

W

S

- Given:
- VAW= 300 km/h
- VWG = 50 km/h
- θ0 = 45°
- Find:
- VAG = ?

An airplane has to fly from city A to city B, located at a distance of 1000 km northeast from A. The speed of the airplane in still air is 300 km/h. To account for the effect of a strong wind blowing at 50 km/h in NE direction (45°) the pilot chooses to head the plane in direction North.

Q. What is the velocity of the airplane relative to the ground?

A – airplane, W – wind, G – ground

Straight line = 180° !!!

Relative motion in 2D: problem solving

- Given:
- VAW= 300 km/h
- VWG = 50 km/h
- θ0 = 45°
- Find:
- VAG = ?

An airplane has to fly from city A to city B, located at a distance of 1000 km northeast from A. The speed of the airplane in still air is 300 km/h. To account for the effect of a strong wind blowing at 50 km/h in NE direction (45°) the pilot chooses to head the plane in direction North.

Q. What is the velocity of the airplane relative to the ground?

Relative motion in 2D: problem solving

- Given:
- VAW= 300 km/h
- VWG = 50 km/h
- θ0 = 45°
- Find:
- VAG = ?

An airplane has to fly from city A to city B, located at a distance of 1000 km northeast from A. The speed of the airplane in still air is 300 km/h. To account for the effect of a strong wind blowing at 50 km/h in NE direction (45°) the pilot chooses to head the plane in direction North.

Q. What is the velocity of the airplane relative to the ground?

Relative motion in 2D: problem solving

- Given:
- VAW= 300 km/h
- VWG = 50 km/h
- θ0 = 45°

After a short stop-over the airplane has to return to city A.

The pilot decides to follow the same route home. Assume that the weather conditions have not changed.

Q. What course should the pilot take?

The subscript rule

Heading

This is the direction you point the vehicle,

This means the direction the vehicle moves relative to the shore

Goes

Parallelogram rule for 2D examples

Cosine rule

Sine rule

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