Vectors and Scalars

• Scalar – a measurement that indicates an amount without specifying direction

• Vector – a measurement that indicates both an amount and a direction

• Why is this important?– Physics requires precision– Distinction between the actual path of an

object and the shortest path from A to B

Where do we see vectors in physics?

• Motion – distance and displacement; speed and velocity– Motion at constant speed (changing directions)– Motion in two dimensions

• With or against a current or wind• With or against gravity

• Forces – direction of a force applied to an object– Objects speed up or slow down in the direction

of the net force

Distance and Displacement

North 20 km

East 15 km

South 8 km

West 20 km

Find the distance traveled = ____

Find the displacement = ___ at ___O

Option 1 – protractor (not bad)

Option 2 – Trig (more accurate)

θ

Heading (bearing) is ____ – θ = _______

Speed and VelocitySouth 32 km

East 24 km Time = 2.5 hours

North 9 km

West 45 km

Find the speed = ____

Find the velocity = ___ at ___O

θ

Heading is _____ + θ = ________

Difference between quantities

• Scalar Quantities (distance, speed)– Indicate size only (metres, km/hr, etc)– Measure the entire path – start to finish

• Vector Quantities (displacement, velocity)– Indicate both size and direction (km/hr [W])– Measure the shortest distance between the starting

and ending points = “as the crow flies”• Calculating Angles – unless the resulting angle

is directly N, S, E, or W, you will– Use trig to determine the angle from start to finish– Convert that angle into a bearing between 0 and 360

degrees (0 = North, 180 = South, etc)

Try these – draw and calculate

1. Walk 25 m [N], then 15 m [W], then 10 m [N], then 5 m [E], finally 15 m [S]

Find both distance AND displacement

2. Drive 60 km [S], then 5 km [W], then 20 km [S], then 25 km [E], then 5 km [N] in 85 minutes

Find both the speed and the velocity (be sure to include the heading)