Non-Perpendicular Vectors
1. A positive charge feels a 1.35 x 10 -6 N force along the +x-axis, and a 2.51 x 10-6 N force along the –y-axis. Find the net
force (the total force) on the charge.
2. A positive charge feels a 1.35 x 10 -6 N force along the +x-axis, and a 2.51 x 10-6 N force at 38.0° below the +x-axis. Find
the net force (the total force) on the charge.
3. A plane flies to city A by going 175km at 30.0° N of E. Then it flies 150.km at 20.0° W of N to city B. Next, it flies 190km
due west to city C. a. Where is the plane, compared to its starting point (how far and in what direction)? b. How far does the
plane need to fly, and in what direction, to get back to its starting point? (Hint: Part b requires a little thinking but not much
work.)
4. A boy and a girl both pull on a heavy box. If the boy pulls with 50.0N of force at 30.0° N of E, and the girl pulls with 45.0N
at 60.0° N of W… a. What one force would replace their two pulls (that is, what is the addition of their forces)? Remember to
include direction. b. They pull on the box but it doesn’t move. Static friction is still holding the box in place. Since the box
doesn’t move (ever), we know the net force (the addition of all of the forces) on the box is 0. How hard must static friction be
pushing on the box, and it what direction?
5. Jim and Sally both leave school from the same spot. Sally walks to Starbucks by walking 150.m at 30.0° W of N. Jim walks
home by walking 140.m at 35.0° N of E. Jim calls Sally and decides to meet her at Starbucks. There is an empty field between
Jim’s house and Starbucks. If he wants to take the shortest route to Starbucks, what direction should he start walking, and how
far will he walk? (Hint: Do NOT add Sally’s and Jim’s walks. You have Jim’s d1. Jim wants to end up where Sally is—that
would be Jim’s dR. You need to find Jim’s d2 so that d1 + d2 = dR . So solve for d2x and d2y and use them to find d2).
Non-Perpendicular Vectors
1. A positive charge feels a 1.35 x 10 -6 N force along the +x-axis, and a 2.51 x 10-6 N force along the –y-axis. Find the net
force (the total force) on the charge.
2. A positive charge feels a 1.35 x 10 -6 N force along the +x-axis, and a 2.51 x 10-6 N force at 38.0° below the +x-axis. Find
the net force (the total force) on the charge.
3. A plane flies to city A by going 175km at 30.0° N of E. Then it flies 150.km at 20.0° W of N to city B. Next, it flies 190km
due west to city C. a. Where is the plane, compared to its starting point (how far and in what direction)? b. How far does the
plane need to fly, and in what direction, to get back to its starting point? (Hint: Part b requires a little thinking but not much
work.)
4. A boy and a girl both pull on a heavy box. If the boy pulls with 50.0N of force at 30.0° N of E, and the girl pulls with 45.0N
at 60.0° N of W… a. What one force would replace their two pulls (that is, what is the addition of their forces)? Remember to
include direction. b. They pull on the box but it doesn’t move. Static friction is still holding the box in place. Since the box
doesn’t move (ever), we know the net force (the addition of all of the forces) on the box is 0. How hard must static friction be
pushing on the box, and it what direction?
5. Jim and Sally both leave school from the same spot. Sally walks to Starbucks by walking 150.m at 30.0° W of N. Jim walks
home by walking 140.m at 35.0° N of E. Jim calls Sally and decides to meet her at Starbucks. There is an empty field between
Jim’s house and Starbucks. If he wants to take the shortest route to Starbucks, what direction should he start walking, and how
far will he walk? (Hint: Do NOT add Sally’s and Jim’s walks. You have Jim’s d1. Jim wants to end up where Sally is—that
would be Jim’s dR. You need to find Jim’s d2 so that d1 + d2 = dR . So solve for d2x and d2y and use them to find d2).