Think about this

• http://www.youtube.com/watch?v=BLuI118nhzc

• 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.

v

sinv

cosv

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

ab

c

Lower case are length of sides

A

B

C Upper case are anglesC

c

B

b

A

a

sinsinsin

Need to learn

The Cosine Rule

If given two sides and an angle between them

ab

cA

B

CBasically when you can spell CAB with your angle and two sides

Abccba cos2222 This bit is like pythagoras

Has an extra bitAlways the 2 sides you have and the angle

The sine and cosine rules

The Sine Rule The Cosine Rule

Need to learn In the formula booklet

C

c

B

b

A

a

sinsinsin Abccba cos2222

Aeroplane ExampleA 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 030o 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?