Vectors

Vectors – Have both magnitude (value) and direction. Scalars – Only have magnitude, no direction Position Velocity Acceleration Force Distance Speed Mass Time

Vectors can be written in two forms: 1. Magnitude and Direction: 20m/s at 50° 2. Component form: < 12.9, 15.3 > m/s

Magnitude and direction form component form 20m/s at 50° = <12.9, 15.3>m/s 50° 270° 180° 90° 0° 20sin50 ≈15.3m/s 20cos50 ≈ 12.9m/s

Magnitude and direction form component form 50m/s at 200° = <-47, -17>m/s 50cos200 ≈ -47m/s 200° 50sin200 ≈ -17m/s

Magnitude and direction form component form <12.9, 15.3>m/s = 20m/s at 50° 20m/s 15.3m/s 50° 12.9 m/s

Magnitude and direction form component form <-40, 20>m/s = 45 m/s at 153° 45m/s 20m/s 153° -27° -40 m/s

Adding Vectors A boat with a speed of 3m/s travels downstream in a river flowing at 4m/s. What is the boats velocity relative to shore? 3m/s 4m/s 4m/s 3m/s 4m/s 3m/s 7m/s

Adding Vectors A boat with a speed of 3m/s travels upstream in a river flowing at 4m/s. What is the boats velocity relative to shore? -3m/s 4m/s 4m/s -3m/s 4m/s -3m/s 1m/s

Adding Vectors A boat with a speed of 3m/s travels straight across a river flowing at 4m/s. What is the boats velocity relative to shore? 4m/s 3m/s

5m/s 3m/s θ 4m/s 3m/s 5m/s θ 4m/s

Adding Vectors A boat with a speed of 3m/s travels at an angle of 60º across a river flowing at 4m/s. What is the boats velocity relative to shore? 4m/s 3m/s 60º

4m/s at 0º = < 4 , 0 > + + = < 1.5 , 2.6 > 3m/s at 60º = < 4 , 0 > 3sin60º =2.6 + + 3m/s at 60º = < 1.5 , 2.6 > 4m/s < 5.5, 2.6 > 3cos60º =1.5 6.08 m/s 2.6 θ 5.5 6.08m/s at 25.3º

3m/s 60º 6.08 m/s 25.3º 4m/s 3m/s 60º 6.08 m/s 25.3º 4m/s

Steps to Add Vectors Draw a diagram. Break all vectors into component form. Add components. Write in magnitude and direction form. Done