Vector Addition
Break (Resolve) each of the following vectors into horizontal (East – West) and Vertical
(North – South) components.
1.
2.
3.
4.
5.
6.
7.
8.
75 N acting at 25o
105 N acting at 95o
150 N acting at 195o
35 N acting at 55o
120 acting at 30o S of W
80 N acting at 45o
190 N acting at 25o E of S
300 N acting at 80o W of S
Find the vector sum for each of the following situations.
9. F1 is 75 N acting at 25o and F2 is 105 N acting at 95o
10. F1 is 150 N acting at 195o and F2 is 35 N acting at 55o
11. F1 is 120 N acting at 30o S of W and F2 is 80 N acting at 45o
12. F1 is 190 N acting at 25o E of S and F2 is 300 N acting at 80o W of S
Solve the following river problems.
13. A boat is able to travel at 5 m/s in still water. You are trying to cross a 500 m wide river with parallel
banks which has a current of 3 m/s. How long does it take to cross the river?
14. A boat is able to travel at 5 m/s in still water. You are trying to cross a 500 m wide river with parallel
banks which has a current of 3 m/s. How far down stream do you land?
15. A boat is able to travel at 5 m/s in still water. You are trying to cross a 500 m wide river with parallel
banks which has a current of 3 m/s. What is your resultant velocity? Hint: you need both magnitude
and direction.
16. A boat is able to travel at 3 m/s in still water. You are trying to cross a 500 m wide river with parallel
banks which has a current of 2 m/s. If you attempt to go directly upstream, what is your velocity relative
to the bank?
17. A boat is able to travel at 9 m/s in still water. You are trying to go directly across a river with parallel
banks which has a downstream current of 5 m/s. What is your resultant velocity?
18. Your boat is able to travel at 7 m/s in still water. You are attempting to cross a river that has a current of
4 m/s. What angle do you need to aim your boat to land directly across the river from your launching
position?
Solve the following incline plane problems.
19. A 50000 N car is parked on a 25o incline. How much force must the brakes apply to keep it in place?
20. A mover is trying to hold a 900 N box on a 10o ramp. How much force should he exert on the box to
hold there?
21. A car weighing 15 000 N rests on a 15o hill. Find the components of the force exerted by the car’s
weight (a) at right angles to the hill (b) parallel to the hill (c) If the car’s brakes were released, which of
these components would move the car downhill?
22. What is the formula for calculating the parallel and perpendicular components for the weight of an
object on an inclined plane if the weight of the object is mg and the angle of the incline is Ө degrees?
23. A 20,000 N car is parked on a hill inclined at an angle of 20 degrees. What are the components of the
car’s weight that are parallel to the hill and perpendicular to the hill? What force must the tires exerted
on the road to keep it from rolling down the hill?
24. A 1000 N TV set is on a ramp inclined at an angle of 25 degrees. What force must a delivery man exert
parallel to the ramp to allow it to move down the ramp at constant speed?