P5b(i) Vectors and Equations of Motion You will find out about Relative Motion The Differences between Scalars and Vectors How to Calculate the Resultant of Two Vectors

Relative Motion Both of these racing cars are travelling at the same speed side by speed. If you were driving one of these racing cars and looked out the window to the other, it would not appear to be moving. Relative to one another they are not moving. The spectators however, do see both cars moving relative from where they sit on their seats. They see them both move very fast in the same direction. Relative means from one point of view On Motorways all the cars are moving at high speed in the same direction. However, relative to each other their relative speed is low. The cars on the other side of the Motorway appear to be moving very quickly in the opposite direction. Their relative speed is very high.

Scalars and Vectors We ask Wile E. Coyote to run at 10m/s. Wile E. Coyote runs off. We tell Wile E. Coyote to stop because we did not state in which direction to run! Speed is a Scalar because it only has one piece of information – magnitude. If we then ask Wile E. Coyote to run at 10m/s in the direction of right then we have provided another piece of information – magnitude AND DIRECTION. This is a vector quantity because it has two pieces of information. Velocity is an example of a vector quantity. Speed is a Scalar. (One piece of info) Velocity is a Vector. (Two pieces of info). S for Speed and S for Scalar. V for Velocity and V for Vector. 50m/s Scalar quantity: Only tells us the magnitude (size of speed). +50m/s Vector quantity: Tells us the magnitude AND direction. Vector quantities may have an arrow OR a +/- sign to indicate direction. Scalar quantities have neither. SCALAR examplesVECTOR examples SpeedVelocity EnergyForce MassAcceleration TimeWeight REMEMBER:

Resultant of Two Parallel Vectors +3m/s + +6m/s = +9m/s Two parallel vectors can be added together algebraically if they are in the same direction OR in the opposite direction. Remember that the arrow size needs to be to scale. +6m/s+-3m/s = +3m/s If the vector quantity is in the OPPOSITE direction we use a – sign to show this. If two parallel vector quantities are in the SAME direction then we ADD THEM. If two parallel vector quantities are in the OPPOSITE direction then we TAKE THEM AWAY. Same = + Opposite = - +3m/s-6m/s = The Resultant Velocity is -3m/s. This can also be expressed as 3m/s in the left direction.

Resultant of Two Non-Parallel Vectors In this example the boat is moving forward with a velocity. The water does not move in the same direction as the boat. The water pushes against the boat at a right angle to the direction the boat is moving. This means that the boat is moving forward but the water pushes against it and causes the boat to move diagonally. In this example the boat is moving across the river from one side to the other. The current pushes down on it. The boat moves diagonally or perpendicularly due to the two forces. 10N 5N ?N 10N 5N R = ?N θ

Questions 1.Winchester is 15 miles from Basingstoke. Which other piece of information do you need to find it? 2.If two cars move at 25m/s in the same direction what is their relative speed? What would their relative speed be if they move in opposite directions? 3.A force of +3N acts on a ball. -1N acts on it in the opposite direction. Calculate the sum of this vector. 4.A rower rows at 2m/s in still water. What is his Resultant velocity if he rows upstream against a current of 3m/s? 5.Find the Resultant of two perpendicular forces of 3N and 14N

Questions