Self-Test: Relative Motion and Vectors Test #1 
Suggested Time: 35 minutes.
1. A boat shown below travels at 4.2 m/s relative to the water, in a river flowing at 2.8 m s. 

At what angle (theta) must the boat head to reach the destination directly across the river? 

A. 34° B. 42° C. 48° D. 56°
2. Pamela swims at 2.8 m/s relative to the water, heading west. The current flows south at 1.2 m/s. Find Pamela's resultant direction. 
A. 23° S of W. B. 25° S of W. C. 23° N of W. D. 25° N of W.
3. An airplane which was flying eastward is later flying southward at the same speed. Which vector shows the airplane's change in velocity? 

4. A pilot points an aircraft due east, while the wind blows from the south. 

The resultant velocity of the aircraft over the ground is 64 m/s, 25° N of E . At what speed does the wind blow? 

A. 2.6 m/s B. 27 m/s C. 30 m/s D. 58 m/s
5. Initial velocity vector Vo and final velocity vector V are shown below. 

Which of the following represents the change in velocity? 

6. A car changes its velocity from 55 km/h due north to 55 km/h due east. What is the direction of the change in its velocity? 
A. 45° north of east. B. 45° north of west. C. 45° south of east. D. 45° south of west.
7. A car travels 10.0 km due east and then 12.0 km in a direct 45° north of west. What is the magnitude of the car's displacement? 
A. 6.6 km B. 8.6 km C. 15.6 km D. 22.0 km
8. A plane heads north with an airspeed of 420 km/h. However, relative to the ground, it travels in a direction 7.0° west of north. If the wind's direction is towards the southwest (45.0° south of west), what is the wind's speed? 
A. 51 km/h B. 65 km/h C. 72 km/h D. 83 km/h
9. A passenger on a bus walks towards the back of the bus at 3.0 km/h, relative to the bus, while the bus travels south at 15 km/h. The passenger's velocity, relative to the road, is: 
A. 18 km/h (N) B. 18 km/h (S) C. 12 km/h (N) D. 12 km/h (S)
10. A motorboat at point X must cross a river flowing as shown in the diagram. If the boat travels at a fixed speed relative to the water, in which direction should the boat head in order to reach the other side in the least amount of time? 
A. 1 B. 2 C. 3 D. 4
11. A boat which can travel at 5.6 m/s in still water heads due east across a river from a dock at X. The boat's resultant path is 32° south of east. 

a) What is the speed of the current? (5 marks) 

b) How long will it take the boat to reach the far shore if the river is 185 m wide? (2 marks)

12. A pilot points an aircraft due west, while the wind blows towards the NNE (45 degrees north of east). The resultant velocity of the aircraft over the ground is 64 m/s, 25° N of W . 

(a) At what speed does the wind blow, and 

(b) what is the speed of the plane with respect to the wind? (7 marks) 

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