<p> TUTORIAL SESSION 3 – Vectors and Motion in 2D and 3D</p><p>1. Explain the difference between a vector and a scalar?</p><p>2. If two vectors add to give zero what can you say about their magnitudes and their directions?</p><p>3. Can the magnitude of the sum of two vectors ever be greater than the sum of the magnitudes of these vectors?</p><p>4. Compare the distance travelled and the displacement for the following paths, the arrows indicate direction of travel.</p><p>C A B</p><p>5. For the points indicated below give the position vector and the distance from the origin.</p><p> y 3 2 C 1 A 0 -4 2 4 5 x -5 -3 -2 -1-1 1 3 B -2 - 3</p><p>1 6. A small town is situated 156 km West and 65 km North of Sydney. How far is it from Sydney?</p><p>7. In a car rally the contestants begin in Melbourne and complete the following journeys: 56 km North, 30 km West then 105 km North, 78 km East Sketch a plot showing the journeys.</p><p> a) How far are they from Melbourne?</p><p> b) If Sydney is 710 km North and 250 km East of Melbourne, how far are they from Sydney?</p><p>8. A boy sitting in a train moving at constant velocity throws a ball straight up into the air. Will the ball land in front of him, behind him or in his hands? Explain.</p><p>9. You are driving behind a truck, going at the same speed as the truck. A crate falls from the truck onto the road. Will your car hit the crate before the crate reaches the ground (you neither swerve nor brake)? Explain.</p><p>10. A dart is thrown horizontally towards the bull’s-eye at an initial speed of 10 m.s-1. If the dartboard is 3 m away where will the dart land relative to the bull’s-eye?</p><p>2 11. A ball rolls off the edge of a table that is 0.9 m high. It strikes the floor 1.5m horizontally away from the edge. a) How long was the ball in the air?</p><p> b) What was the initial speed of the ball?</p><p>12. A boy kicks a soccer ball with an initial angle of 30° to the horizontal and an initial speed of 25 m.s-1. a) What height does the ball reach?</p><p> b) How far does it travel in the horizontal direction?</p><p>13. A cannon has a muzzle velocity of 85 m.s-1. If it is aimed at 40° to the horizontal what is the range of the cannon?</p><p>14. A volcano that is 3300 m above sea level erupts and sends rock fragements hurtling into the sea 9.4 km away. If the fragements were ejected at an angle of 35° what was their initial speed?</p><p>15. A boat is travelling upstream at 14 km.h-1 with respect to the water of a river. The water itself is flowing at 9 km.h-1 with respect to the ground. a) What is the velocity of boat with respect to the ground?</p><p>3 b) If a child on the boat walks from the front to the rear at 6km.h-1 with respect to the boat, what is the child’s velocity with respect to the ground?</p><p>16. Snow is falling vertically at a constant speed of 8.0 m.s-1. A man is driving at a constant speed of 20 m.s-1. At what angle do the snowflakes appear to be falling?</p><p>Student Learning</p><p>How has your grasp of these concepts changed since the previous tutorial?</p><p>4</p>