I have this mechanics problem. Please help me solve it.

Rory, Aurora and Raoul are three lions fi�ghting over a piece of meat of mass 12
kg.
Each lion exerts a horizontal pull. Rory pulls with a force of 800 N.
Aurora, who is 120degrees to Rory's right, exerts a force of 400 N.
Raoul is 140 degrees to Rory's left.
The meat accelerates in Rory's direction.
(a) Find the force which Raoul is exerting.

Thank you in advance.

Let F-Raoul be the force exerted by Raoul.

Consider the direction perpendicular to Rory's direction,
There is no nett force in that direction as there is no movement along it.
F-Raoul Cos(40º) = 400 N * Cos(60º) ------> F-Raoul = 261 N
Nett force in Rory's direction = 800 N - 261 N * Sin(40º) - 400 N * Sin(60º).
You just apply F = m*a to find the acceleration.

In the case of resolving the force perpendicular to Rory's direction, isnt it suppose to be F-Raoul cos(50º) = 400 cos(30º) ?

To solve this mechanics problem, we can use vector addition to find the net force acting on the piece of meat.

Step 1: Draw a diagram to visualize the situation. Label Rory's force as 800 N, Aurora's force as 400 N, and the angle between them as 120 degrees. Also, label the angle between Rory and Raoul as 140 degrees.

Step 2: Break down Rory's force into horizontal and vertical components. Since we're only interested in the horizontal direction, we'll focus on that. The horizontal component of Rory's force can be found using trigonometry:

Horizontal component of Rory's force = 800 N * cos(0 degrees) = 800 N

Step 3: Break down Aurora's force into horizontal and vertical components. Since Aurora is 120 degrees to Rory's right, we need to find the horizontal component of her force. Again, we'll use trigonometry:

Horizontal component of Aurora's force = 400 N * cos(120 degrees) = -200 N (negative because it is in the opposite direction of Rory)

Step 4: Now, let's find Raoul's force. Since the meat is accelerating in Rory's direction, the net force in that direction is positive. This means Raoul's force and Rory's force need to add up to the net force. We can calculate Raoul's force using vector addition:

Net horizontal force = Rory's horizontal force + Aurora's horizontal force + Raoul's horizontal force

800 N + (-200 N) + Raoul's horizontal force = net horizontal force

Raoul's horizontal force = net horizontal force - 800 N + 200 N

Raoul's horizontal force = net horizontal force - 600 N

Since we're looking for the force exerted by Raoul, we don't know its magnitude or direction yet.

Step 5: Substitute the given values into the equation. Since we don't have the exact value for the net horizontal force, we'll use a variable to represent it. Let's call it F_net.

Raoul's horizontal force = F_net - 600 N

And that's it! You now have the mathematical equation to find the force exerted by Raoul. You'll need to know the value of the net horizontal force or be given additional information to solve for Raoul's force.