A. Describing Vectors

A. Describing Vectors 1. Describe the vector below.

2. Describe the vector below.

3. Draw the following vectors on the coordinate systems below. a. A 4 m/s2 vector acting 40o South of East. b. A 10 m/s vector acting due West. c. A 7 N (Newton) vector acting @ 120o.

1. 2 m/s @ 20o North of West 2. 15 N @ 240o or 15 N @ -120o 3. See Instructor

B. Vector Components

1. A plane travels 300 km in a direction 40° North of East. 1.a. What is the North/South component of the plane’s displacement? 1.b. What is the East/West component of the plane’s displacement? 2. A heavy box is pulled across the floor by a rope. The rope makes an angle of 60° with respect to the horizontal, and the tension in the rope is 80 N. What is the horizontal component the force pulling the box across the floor?

3. A push mower is pushed to the right across a lawn by a person pushing down at an angle, along the mower handle, with a force of 90 Newtons. 3.a. What are the vertical and horizontal components of the force if the mower handle forms an angle of 60° below the horizontal? 3.b.What are the vertical and horizontal components of the force if the mower handle forms an angle of 30° below the horizontal?

4. A 200 N force acts on a tire swing at an angle 35° South of West. 4.a. What is the North/South component of the force? 4.b.What is the East/West component of the force?

1. a) 192.8 km b) 229.8 km 2. 40 N

3. a) Fx = 45 N Fy = −77.94 N 4. a) −114.7 N b) −163.8 N b) Fx = 77.94 N Fy = −45 N

C. 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. 1.a. What is the magnitude and direction of the resultant force? 1.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. 2.a. What is the distance walked by the hiker? 2.b.What is the displacement of the hiker from the starting point?

3. A boat heads directly across a river 40 m wide that has a current flowing downstream at 3.8 m/s. The boat can travel at a speed of 8 m/s in still water. 3.a. If the boat tries to go straight across the river, what will be its resultant velocity with respect to the shoreline? 3.b.How long does it take the boat to cross the river? 3.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, 36.87° East of North 2. a) 20 km b) 100 N, 36.87° West of South b) 14.14 km, 45° North of West 3. a) 8.857 m/s, 64.59° w/ respect to the shoreline 4. 78.31 km, 46.71° North of East b) 5 s c) 19 m 6. 162.2 km/h, 47.88° South of East

D. Adding Multiple Vectors

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 1.a. What is the x-component of the resultant force? 1.b. What is the y-component of the resultant force? 1.c. What is the magnitude and direction of the resultant force? 1.d. What is the magnitude and direction of the equilibrant force?

2. (III) A sign that weighs 150 N hangs in a state of equilibrium and is supported by two cables (A and B) as shown below. What is the tension force in each cable?

1. a) −11.84 N b) −31.21 N c) 33.38 N @ 249.2° d) 33.38 N @ 69.22° 2. A= 134 N B= 110 N