Vectors

Q1. Find the resultant of two forces 25 N and 20 N with an angle of 60° between them.

What is the angle between the resultant and the first force?

Using graph paper you can construct the vector diagram as shown above.

Make sure that you clearly indicate the scale you are using for the vector magnitude.

Also make your answer stand out clearly to the examiner.

To solve by calculation you need to resolve each of the vectors into their horizontal and vertical components:

Vector A only has a horizontal component = 25

Its vertical component = 0

Vector B has a horizontal component of 20 cos 60^o = 10

and a vertical component of 20 sin 60^o = 17.3

Adding the vectors A and B we get the Resultant R:

horizontal component = 25 + 10 = 35

vertical component = 17.3

Using pythagoras:

35² + 17.3² = R²

R² = 1524.29

R = 39

The magnitude of the resultant R = 39 N

From the diagram:

tan α = 17.3/35 = 0.494

α = 26^o

The angle between the resultant and the first force is 26^o