Question

find the resultant of two forces one 6N due east other 8N due north​

Answer 1

Here the angle between the two forces, one of 6N due east and the other of 8N due north, is 90°.

Let the resultant force be R. Then,

Magnitude of the resultant force is,

R = √(6² + 8² + 2 × 6 × 8 × cos 90°)

R = √(36 + 64)

R = √100

R = 10 N

And the direction of the resultant force is,

α = arctan [(8 sin 90°) / (6 + 8 cos 90°)]

α = arctan (4 / 3)

α = 53°

Hence the resultant force is 10 N from East at 53° towards North.

Answer 2

The resultant force of two forces one 6 N due east and the other 8 N due north​ is 10 N from East at 53° towards North.

Given: one force of 6 N due east and another force of 8 N due north

To Find: the resultant of two forces

Solution:

According to the map, we understand that angle between east and north is 90°. So the angle between the forces is also 90°.

Let the resultant force be R. Then, the magnitude of the resultant force is,

R = √(6² + 8² + 2 × 6 × 8 × cos 90°)                        [ cos 90° = 0 ]

R = √(36 + 64)

R = √100

R = 10 N

And the direction of the resultant force can be found using formula;

α = arctan [( b × sin Ф ) / ( a + b × cos Ф)]  

here, a = 6 N and b = 8 N.

α = arctan [(8 × sin 90°) / (6 + 8 × cos 90°)]

α = arctan (4 / 3)

α = 53°

Hence the resultant force of two forces one 6 N due east and the other 8 N due north​ is 10 N from East at 53° towards North.

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