# Relative motion of objects in two dimensions

• Analyse the relative motion of objects in two dimensions in a variety of situations, for example:
– a boat on a flowing river relative to the bank
– two moving cars
– an aeroplane in a crosswind relative to the ground

Learn.

When you are sitting in a car travelling down the highway at 100 km/ h you are stationary right? Well it depends on a thing called your frame of reference. Your frame of reference is the point which you chose to be the thing you are moving relative to. If you are choosing the car as your frame of reference, you are stationary. If you choose the road as your frame of reference your traveling at the speed the odometer says.

What if your travelling along side someone. Your going 100 km/ h and they are going 105 km/ h from their frame of reference your moving 5km/h backwards and from your frame of reference they’re moving 5 km/h forwards.

The formula to calculate your velocity relative to another’s velocity:

velocity the frame of reference – velocity of the object = velocity of the object relative to the frame of reference.

The way I approach these problems is to imagine I am sitting in the frame of reference and thinking logically what the speed of the object would be from where I am. If it says relative to, that just means that is where your are observing it from – so it is where you would be sitting.

Food for thought: Light has a universal speed limit of 299 792 458 m/s, would this speed limit be dependent on a frame of reference – what if the other frame of reference is light moving in the opposite direction.

Memories.

Velocity the frame of reference – velocity of the object = velocity of the object relative to the frame of reference.

Master.

Question 1.

A) A boat is floating on a flowing river, the river is moving at 10 km/h. What is the speed of the boat relative to the bank.

B) A boat is floating on a flowing river, the river is moving at 10 km/h. What is the speed of the bank relative to the boat.

Question 2.

Two cars are moving towards one another, The car moving to the right is travelling at 50 km/h and the car moving to the left is travelling at 40 km/h. What is the speed of the car moving to the right relative to the car moving to the left?

Question 3.

An airplane has head winds which are moving 60 km/h, it is travelling relative to these head winds at 550 km/h. Explain what its speed of the plane relative to the ground?