Download Vectors Problem Set 1

Physics 1
Vectors
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Vectors Problem Set 1
A. Vector Components
1. A plane travels a distance of 300 km in a direction 40o North of East.
a. What is the North component of the plane’s motion?
b. What is the East component of the plane’s motion?
2. A heavy box is pulled across the floor by a rope. The tension force in the rope is
80 N and the rope forms an angle of 60o with respect to a horizontal reference
line. What is the magnitude of the force that is pulling the box across the floor?
3. A push mower is pushed across a lawn using a force of 90 N that acts along the
mower handle.
a. What are the vertical and horizontal components of the force if the
mower handle forms an angle of 60o with the horizontal?
b. What are the vertical and horizontal components of the force if the
mower handle forms an angle of 30o with the horizontal?
4. A 200 N force acts at an angle 35o South of West.
a. What is the South component of the force?
b. What is the West component of the force?
1. a) 193 km b) 230 km
3. a) Fx = 45 N Fy = -78 N
b) Fx = 78 N Fy = -45 N
2. 40.0 N
4. a) -115 N b) -164 N
B. Adding Vectors
1. Two forces act concurrently on point P. One force is 60 N acting due East, the
other force is 80 N acting due North.
a. What is the magnitude and direction of the resultant force?
b. What is the magnitude and direction of the equilibrant force?
2. A hiker leaves camp and walks 10 km due North and 10 km due West.
a. What is the distance walked by the hiker/
b. What is the displacement of the hiker from the starting point?
3. A boats heads directly across a river 40 m wide that has a current flowing at
3.8 m/s. The boat can travel at a speed of 8 m/s in still water.
a. If the boat tries to go straight across the river, what will be its resultant
velocity with respect to the shoreline?
b. How long does it take the boat to cross the river?
c. How far downstream (in relation to the starting point) is the boat after is
crosses the river?
4. A salesperson leaves the office and drives 26 km due North along a straight
highway. He then turns onto a road that leads in a direction 30o North of East and
travels for an additional 62 km. What is the displacement if the salesperson from
the office?
5. An airplane flies at 150 km/h in a direction 30o South of East. At the same time a
50 km/h wind blows the plane in a direction 25o West of South. What is the plane’s
resultant velocity with respect to compass points on the Earth?
1. a) 100 N @ 37o East of
North
b) 100 N @ 37o West of
South
4. 78.3 km @ 43.3o East of
North
2. a) 20 km
b) 14.1 km @ 45o North of
West
3. a) 8.9 m/s @ 65o
b) 5 s
c) 19 m
5. 162 km/h @ 47o
South of East
C. Adding Multiple Vectors / Equilibrium
1. The following forces act concurrently on point P.
A: 10 N @ 0o
B: 20 N @ 110o
C: 15 N @ 180o
D: 50 N @ 270o
a. What is the magnitude and direction of the resultant?
b. What is the magnitude and direction of the equilibrant?
2. A 150 N sign hangs in a state of equilibrium and is supported by two cables that
have an angle of 120o between them. What is the tension force in each cable?
150 N
1. a) 33.4 N @ 249o b) 33.4 N @ 69.3o
2. Tension in each cable is 150 N.