Think about this hzc hzc A ball is fired out the back of a car. It is fired.

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Presentation transcript:

Think about this hzc hzc A ball is fired out the back of a car. It is fired at the same speed the car is moving. What happens to the ball?

Resultant Velocities To be able to set up right angled vector triangles. To be able to use Pythagoras and trigonometry to find out unknown values.

Resultant velocities Since velocity is a vector, these can be added on to make a resultant velocity Use Pythagoras to find resultant velocities

SOHCAHTOA with vectors You can also turn a vector into horizontal and vertical components.

Example A motorboat is travelling 4ms -1 East & encounters a current travelling 3ms -1 North, the river is 80m wide. a)What is the resultant velocity of the motorboat? b)How long does it take to reach the other bank? c)What distance downstream does the boat reach the opposite bank?

Exam Questions I would like you to try and apply what you know to answer the past exam questions. For each question draw a clear diagram and label all the relevant information. Get your answers regularly checked and ask for support when needed.

Jan 2006

Jan 2007

Jan 2008

June 2009

June 2010

Resultant Using i and j A model plane is flying with a constant velocity of (5i – j)ms -1 relative to the air. A wind with velocity (-i + 2j)ms -1 is blowing. Find the magnitude of the resultant velocity and the angle it makes with the vector i.

Independent Study Watch the video on resultant velocity for non- right angled triangles. Make sure you are familiar with the sine and cosine rules. Mechanics 1 textbook: Chapter 2 Exercise E - Pages 41-42

Resultant Velocities Know how to find resultant velocities with a non-right angle triangle

Non-right angle triangles Can no longer use Pythagoras. What can we do?

The Sine Rule If given two sides and their corresponding angles, we can see the sine rule Lower case are length of sides Upper case are angles Need to learn

The Cosine Rule If given two sides and an angle between them Basically when you can spell CAB with your angle and two sides This bit is like pythagoras Has an extra bit Always the 2 sides you have and the angle

The sine and cosine rules The Sine RuleThe Cosine Rule Need to learnIn the formula booklet

Aeroplane Example A plane with an airspeed of 250kmh -1 has to fly from town A to town B, 100 km due east of town A. A wind is blowing from 030 o at 50 kmh -1 (a) Sketch a velocity triangle relating to the above (b) Find the direction the plane must be headed (c) How long will it take for the plane to travel from A to B?

Aeroplane Example A plane with an airspeed of 250kmh -1 has to fly from town A to town B, 100 km due east of town A. A wind is blowing from 030 o at 50 kmh -1 (a) Sketch a velocity triangle relating to the above (b) Find the direction the plane must be headed (c) How long will it take for the plane to travel from A to B?