# Worksheet: Resolution of Forces into Two Given Directions

In this worksheet, we will practice solving problems on the resolution of a force into two directions using the properties of a parallelogram and applying the sine rule.

Q1:

The diagram shows a body of weight 69 N suspended by 2 light, inextensible strings, and . Both strings make an angle of with the horizontal. Resolve the weight of the body into two components in the direction of and in the direction of . Give your answers to the nearest newton.

• A ,
• B ,
• C ,
• D ,

Q2:

A force of magnitude 96 N acts vertically downwards. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q3:

A force of magnitude 41 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and . Give your answer to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q4:

The angle between two forces, and is . Their resultant is 2,900 N and makes an angle of with . Find the forces and . Give your answers to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q5:

A force of magnitude 99 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places.

• A ,
• B ,
• C ,
• D ,
• E ,

Q6:

A force , acting in a northerly direction, is the resultant of two forces and . The force has a magnitude of 172 N and is acting north of east, and the force acts in a westerly direction. Find the magnitudes and .

• A ,
• B ,
• C ,
• D ,

Q7:

The diagram shows a body of weight 58 N suspended by 2 light, inextensible strings, and . Both strings make an angle of with the horizontal. Resolve the weight of the body into two components in the direction of and in the direction of . Give your answers to the nearest newton.

• A ,
• B ,
• C ,
• D ,

Q8:

The diagram shows a body of weight 54 N suspended by 2 light, inextensible strings, and . Both strings make an angle of with the horizontal. Resolve the weight of the body into two components in the direction of and in the direction of . Give your answers to the nearest newton.

• A ,
• B ,
• C ,
• D ,

Q9:

A force of magnitude 59 N acts vertically downwards. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q10:

A force of magnitude 27 N acts vertically downwards. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q11:

A force of magnitude 89 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and . Give your answer to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q12:

A force of magnitude 10 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and . Give your answer to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q13:

A force of magnitude 137 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places.

• A ,
• B ,
• C ,
• D ,
• E ,

Q14:

A force of magnitude 157 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places.

• A ,
• B ,
• C ,
• D ,
• E ,

Q15:

The angle between two forces, and is . Their resultant is 6,200 N and makes an angle of with . Find the forces and . Give your answers to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q16:

The angle between two forces, and is . Their resultant is 2,600 N and makes an angle of with . Find the forces and . Give your answers to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q17:

A force , acting in a northerly direction, is the resultant of two forces and . The force has a magnitude of 186 N and is acting north of east, and the force acts in a westerly direction. Find the magnitudes and .

• A ,
• B ,
• C ,
• D ,