Self-Test: Relative Motion and Vectors Test #2 
Suggested Time: 50 minutes.
 
1.

Two velocity vectors, v1 and v2 are shown.

Which of the following best represents the resultant of the addition of the two velocity vectors?
 

A. B.
C. D.
 
2.

A car travelling north at 20 m/s is later travelling west at 30 m/s. What is the direction of the change in velocity?

A. B. C.. D.
 
3. Vectors P and Q in the grid below represent velocities. Each side of each little square in the grid represents a speed of 1 m/s.

Let vectors P and Q represent the initial and final velocities respectively of a particle over a 4.0 s time interval. Then the magnitude of the average acceleration during this interval is:

 

A. 3.25 m/s2 B. 3.45 m/s2 C. 3.75 m/s2 D. 13 m/s2 E.15 m/s2

 

4. The vector in the diagram at right is equivalent to: 


 

A. B. C. D. E.
 
5. In the following diagram, the boat has a speed of 4.5 m/s in still water. 

How long will it take to travel the 2000 m to the north-south meridian as shown in the above diagram?

 

A. 444 s B. 543 s C. 630 s D. 775 s

 

6.

A car travelling at 80 km/h encounters a train 1.2 km in length moving in an opposite direction at 50 km/h. What distance does the car travel while the train passes by?

A. 0.60 km B. 0.74 km C. 1.2 km D. 1.9 km E. 3.2 km

 

7.

A gun is pointing vertically downward from an airplane moving with a constant horizontal velocity of 240 m/s. If the gun fires a bullet with an initial speed of 280 m/s relative to the gun, which of the following describes the initial direction of the bullet with respect to the ground?

A. Vertically downward

B. Horizontal in the direction of the plane's motion

C. 41° below the horizontal

D. 49° below the horizontal

 

8.

How long does it take an automobile traveling in the left lane at 50.0 km/h to pull alongside a car traveling in the right lane at 32.0 km/h if the cars' front bumpers are initially 140 m apart?

A. 28.0 s B. 6.15 s C.7.78 s D. none

 

9. A boat requires 2.00 min to cross a river that is 150 m wide. The boat's speed relative to the water is 3.00 m/s and the river current has a speed of 2.00 m/s. At what possible upstream or downstream points does the boat reach the opposite shore? (6 marks)

 

10. An aircraft with an airspeed of 250 km/h heads 19° east of north. When it encounters a wind, its velocity relative to the ground becomes 260 km/h due north.

(a) Write the vector equation for the velocity of wind with respect to earth. (1 mark)

(b) Sketch a vector diagram reflecting the above vector equation. (2 marks)

 
11.

An aircraft heads due south with a speed relative to the air of 44 m/s. Its resultant speed over the ground is 47 m/s. The wind blows from the west.

a) What is the speed of the wind? (4 marks)

b) What is the direction of the aircraft’s path over the ground? (3 marks)

 

12. Two ships A and B, leave port at the same time. A travels at 24 km/h in a direction 450 north of west, and ship B travels at 28 km/h in a direction 50o south of west.

a) Write the vector equation for the velocity of boat A relative to boat B. (1 mark)

b) Draw the vector diagram (use a ruler) that accurately represents the vector equation. Clearly label the vectors and known angles! (2 marks)

c) What is the velocity of ship A relative to ship B? (4 marks)

 

13. A pilot wishes to reach a destination 1800 km away at an angle 65o West of South, but quickly discovers that due to a wind of 80 km/h blowing at 55o North of East, adjustment to the heading will need to be made. What must be the planes velocity with respect to the wind if it is to arrive at its destination in 3.0 hours?

a) Write the vector equation for the velocity of the plane with respect to the wind. (1 mark)

b) Draw the vector diagram (use a straight edge) that accurately represents the vector equation. Clearly label the vectors and known angles! (2 marks)

(c) What is the velocity of the plane with respect to the wind? (5 marks)

 
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