# Vectors Worksheet

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Vectors Worksheet

Part I: The Basics

1. Use the terms scalar and vector to compare (similarities) and contrast (differences) the
following situation. An airplane flies 110 km due west from an airport and
another airplane flies 110 km due east from the same airport.

2. Vector d has a magnitude of 15.5 m and is pointed down into the lower left quadrant
of an x-y axis at an angle of 23˚ to the negative x-axis. Find the x and y, (that is,
the dx and dy, components) of this vector.

3. Vector v has components vx and vy. If vx = 10.1 m/s and vy = -13.1 m/s, what is the
magnitude and direction of the resultant vector (vr)?

Draw a diagram for each scenario.

1. After walking 11 km due north from camp, a hiker then walks 11 km due east.
a. Calculate the total distance walked by the hiker?
b. Calculate the total displacement from the starting point.

2. Two students push on a box. One pushes with a force of 125 N to the east and the other
exerts a force of 165 N to the north.
a. Draw a line to indicate the direction in which the box will move.
b. Calculate the magnitude of the resulting force on the box.
c. Calculate the number of degrees north of east (the degrees above the horizontal)
of the resultant force.

3. Dr Cornelis, on his trip in the Arctic Circle, was driven 13 km due east, then 18 km
north and finally 3 km west.

a. What is the total distance Dr Cornelis was driven?
b. What is the resulting displacement of Dr Cornelis from the starting point?
(Hint: draw the arrow for the displacement and then “find” a right triangle you
can use to determine the displacement.)

4. You and a friend start from the same point; you walk 15 meters in the direction 50˚
west of north, and your friend walks 20 m in the direction 40˚ east of north. What
is your displacement from your friend at the end of the walk?
5. Meg’s pet guinea pig, Pomegranate, leaves our apartment and wanders the neighborhood
following this route: He travels four blocks east, three blocks north, three blocks east, six blocks
south, three blocks west, three blocks south, two blocks east, two blocks south, eight blocks west,
six blocks north and two blocks east. At the end of his trip, where is Pomegranate relative to his
starting point (what is his displacement)?
Part III: Vector Resolution

2. A ship sails 10 km in a northeast direction (45˚ north of the positive x-axis). What are
the components of its displacement to the north and to the east?

3. 4. What are the north and east components of a velocity vector of magnitude 100
km/h and 30˚ west of south?

4. A heavy box is pulled across a wooden floor with a rope. The rope makes an angle of
60˚ with the floor. A force of 75 N is exerted on the rope. What is the component
force parallel to the floor?

5. An airplane flies toward 149˚ at 525 km/h. What is the component of the airplane’s
velocity

a. toward 90˚
b. toward 180˚?

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