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PHYSICS 11 VECTORS WORKSHEET
1. Use graph paper to find the resultant vector from the combinations listed:
C D G
A B E F
a) A+E ; b) D+F; c) B+C+G; d) F+C+A; e) E+D+G; f) A-C; g) D-F
2. Use graph paper to determine the magnitude of displacement of a car that travels:
a) 10 km due east and then 12 km at 45 north of west.
b) 10 km due south, 2 km due west, then 5 km due east.
c) 8 km due north, 4 km due east, then 6 km at 30 south of west.
3. Calculate the displacement (magnitude and direction) of a car that travels:
a) 3.0 km due north, then 4.0 km due east.
b) 12.5 km due south, then 6.8 km due west.
c) 10 km due south, 2 km due west, then 5 km due east.
4. Two budding physics students perform an experiment. Student A pushes a crate along a
very slippery ice surface with a force of 25 N due south, while student B pushes on the same
crate with a 40 N force due west. What is the net force acting on the crate (magnitude and
direction)?
5. An aircraft heading due west at 48 m/s encounters a wind blowing towards the south at 27 m/s.
What is the resultant velocity (speed and direction) of the aircraft?
6. A boat is headed directly across a river at 7.8 m/s due north, while the river’s current travels at
3.2 m/s due east. All speeds are relative to a point on shore.
a) What is the velocity of the boat (speed and direction) relative to shore?
b) If the river is 820 m wide, how far downstream does the boat end up, once across?
7. An athletic physics student (there are a few) is capable of swimming at 2.1 m/s in still water.
She wishes to directly cross a river that has a 1.4 m/s current and reach point X, as shown below.
X
river
current 1.4 m/s
o starting
point
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a) Explain what would happen if the student were to try to swim directly across to X.
b) At what angle (from the dotted line) should the student swim in order to end up at X?
c) What will be the resultant speed?
8. A wagon is pulled as shown below: F = 85 N
25
a) Determine the horizontal and vertical
components of the force shown.
b) If the cart were travelling at constant speed,
what would be the acting friction force?
9. An jet aircraft is travelling 310 m/s at 35 south of east. What is the south component of
its velocity?
10. An arrow is shot at 35 m/s into the air at an angle of 40 to the horizontal. Determine the vertical
and horizontal components of its speed.
11. Three physics students are fighting over a graphing calculator. Student A pulls on the
calculator with a force of 15 N north, while student B pulls with a 35 N force east. What force,
and in what direction, must student C apply to the calculator if it is to remain stationary
(i.e. the net force = 0)?
12. Examine the diagram to the right.
Determine the tension T1 in the
right cable. 45
T1 = ?
450 N
1. a) 5 right, 3 up b) 13 left, 3 up c) 2 left, 1 up d) 1 right, 5 up e) 7 left, 1 up f) 3 right, 9 up g) 1 left, 5 down 2. a)
8.6 km b) 10.4 km c) 3.2 km 3. a) 5.0 km at 53 E of N b) 14.2 km at 29 W of S c) 10.4 km at 17 E of S 4. 47.2
N at 32 S of W 5. 55 m/s at 29 S of W 6. a) 8.4 m/s at 22 E of N 7. b) 42 c) 1.6 m/s
8. a) 77 N, 36 N b) 77 N to the left 9. 178 m/s 10. 22 m/s, 27 m/s 11. 38 N at 23 S of W 12. 636 N