TUTORIAL SESSION 3 Vectors and Motion in 2D and 3D

TUTORIAL SESSION 3 – Vectors and Motion in 2D and 3D

1. Explain the difference between a vector and a scalar?

2. If two vectors add to give zero what can you say about their magnitudes and their directions?

3. Can the magnitude of the sum of two vectors ever be greater than the sum of the magnitudes of these vectors?

4. Compare the distance travelled and the displacement for the following paths, the arrows indicate direction of travel.

5. For the points indicated below give the position vector and the distance from the origin.

y 3 2 C 1 A 0 -4 2 4 5 x -5 -3 -2 -1-1 1 3 B -2 - 3

1 6. A small town is situated 156 km West and 65 km North of Sydney. How far is it from Sydney?

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.

a) How far are they from Melbourne?

b) If Sydney is 710 km North and 250 km East of Melbourne, how far are they from Sydney?

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.

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.

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?

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?

b) What was the initial speed of the ball?

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?

b) How far does it travel in the horizontal direction?

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?

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?

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?

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?

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?

Student Learning

How has your grasp of these concepts changed since the previous tutorial?