Vectors Worksheet
Name ________________________
1) What two quantities do vectors possess?
a) _________________________
b) ___________________________
Measure the magnitude of the vectors below in centimeters and draw the resultant to scale under the
individual vectors including its length in cm.
2)
magnitude _________________ direction ____________
3)
magnitude __________________ direction ___________
4)
magnitude __________________ direction ___________
5)
magnitude __________________
6)
magnitude ________________
7)
magnitude ____________________
Vector Problems
For the following problems
a. Draw a sketch of the vectors with angles if necessary
b. SHOW ALL WORK AND UNITS IN YOUR CALCULATION
c. Circle your answer
Finding Resultant Magnitude and Direction
1. A boat leaves a dock and sails north at a velocity of 10.4 m/s (relative to the water) while a current
carries it due east at 6.7 m/s. What is the resultant velocity and angle of the boat relative to an
observer on a dock?
2. A rocket accelerates horizontally 25 m/s2 while at the same time gravity accelerates downward at a
rate 9.80 m/s2. What is the resultant acceleration? Include the angle.
3. Jane pushes a box with 60 Newtons of Force due west, while Jim pulls the box south with a force
of 42 Newtons. What is total force on the box? Include the angle in which the force is applied.
4. A small plane is seen moving at 90 m/s to the east while drifting south at a speed of 30 m/s due to
high winds. What is the net velocity?
5. Emily passes a soccer ball 6.0 m directly across the field to Kara. Kara then kicks the ball 14.5 m
directly down the field to Luisa. What is the ball’s total displacement as it travels between Emily
and Luisa?
Resolving Vectors into Components
1. A person walks 200 m at an angle of 27 North of East. What are the horizontal and vertical
components of the displacement?
2. A car moves 60 m/s at an angle of 35 West of South. What are the horizontal and vertical
components of the displacement?
3. A cannonball is launched with a speed of 170 m/s at 40 above the horizontal. What are the
horizontal and vertical components of the displacement?
4. How fast must a truck travel to stay beneath an airplane that is increasing in altitude at a velocity of
105 km/h at an angle of 25 relative to the ground?
5. What are the horizontal and vertical components of a cat’s displacement when the cat climbed 5 m
directly up a tree?
Adding Vectors
1. A football player runs directly down the field for 35 yards before making a cut to the right at an
angle of 25 from his original direction and running an additional 15 yards before getting tackled.
What is the magnitude and direction (include angle) of the runner’s displacement?
2. A plane travels 2.5 km at an angle of 35 to the ground then changes direction and travels 5.2 km at
an angle of 22 to the ground. What is the magnitude and direction (include angle) of the plane’s
total displacement?
3. During a rodeo, a clown runs 8.0 m to the north, turns 55 north of east and runs 3.5 m. Then, after
waiting for the bull to come near, the clown turns due east and runs 5.0 m to exit the arena. What is
the clown’s resultant displacement?
4. A shopper pushes a cart 40 m south down one aisle and then turns 90 moves 15 m. He then makes
another 90 turn and moves 20 m. Find the shopper’s resultant displacement.
5. A person walks in a path shown in the diagram below. What is the person’s resultant displacement?
Extension Questions
1. A firefighter sprays water from a hose at a velocity of 40 m/s at an angle of 37 relative to the
ground. He is spraying the top floor of the building. What is the height of the building?
2. During a thunderstorm, a tornado lifts a car to a height of 125 m above the ground. Increasing in
strength, the tornado flings the car horizontally at a speed of 90.0 m/s. How long does it take the
car to reach the ground? How far horizontally does it travel before hitting the ground? (hint: think
about this problem in terms of x and y components and keep them separate.)