advertisement

Vectors Vectors – Have both magnitude (value) and direction. • • • • Position Velocity Acceleration Force Scalars – Only have magnitude, no direction • • • • 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 20m/s at 50° = component form <12.9, 15.3>m/s 90° 20sin50 ≈15.3m/s 180° 50° 20cos50 ≈ 12.9m/s 270° 0° Magnitude and direction form 50m/s at 200° = <-47, -17>m/s 50cos200 ≈ -47m/s 50sin200 ≈ -17m/s 200° component form Magnitude and direction form component form <12.9, 15.3>m/s = 20m/s at 50° m v 12.9 15.3 20 s 15.3 tan 12.9 1 15.3 tan 12.9 50 2 20m/s 15.3m/s 50° 12.9 m/s 2 Magnitude and direction form component form <-40, 20>m/s = 45 m/s at 153° m v (40) 20 45 s 2 20m/s 45m/s -27° 153° -40 m/s 2 20 tan 40 1 20 tan 40 27 180 27 153 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? 4m/s 3m/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? 4m/s -3m/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 5m/s 3m/s θ 4m/s m v 3 4 5 s 2 2 3 tan 4 1 3 tan 4 37 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 60º 3sin60º =2.6 4m/s 60º 4m/s at 0º + 3m/s at 60º = < 4 , 0 > + + = < 1.5 , 2.6 > < 5.5, 2.6 > 3cos60º =1.5 m v 5.5 2.6 6.08 s 2 2.6 θ 5.5 2.6 tan 5 .5 1 2.6 tan 5. 5 25.3 6.08m/s at 25.3º 2 25.3º 4m/s 60º 25.3º 4m/s 60º Steps to Add Vectors • • • • • • Draw a diagram. Break all vectors into component form. Add components. Draw a diagram. Write in magnitude and direction form. Done