Urgent Physics help please!?

Can people help me solve these problems please? I know it's a nuisance but I'm so lost. There must be at least one expert out there … All help will be greatly appreciated! = D Oh, and it would be helpful if you can show me how you have the answer. 1. Why is it easier to pull a sled with a rope, 2 m which is pushing with a stick of 2 m? (Assume that both the rope and the pole are at the same angle to the ground the surface) 2. A ship sails 10 km on a course of 320 degrees. What are the components of its displacement towards the east? 3. Two forces 80n and 100N acts at an angle of 60 degrees apart, throwing an object. What is the size of the single force that would replace the forces gives? (Solve for the vector diagram) 4. A yacht is sailing north in 7ms-1 and the wind blows from the west at 4 ms-1. What is the relative speed to sail the boat with the wind? Thanks!

1) A rope is lighter than a post, which reduces the amount of work required to move the sled lighter. (Not sure if this answer is correct.) 2) 320 degrees taking is the same as 40 degrees west of north. So if you draw a vector of 10 km in that direction, the component x is x = – (10 km) without (40) = -6.43 km. You can also change the angle to the polar form. CAC measured from the + x axis. You get 130 degrees. Then: x = (10 km) cos (130) = -6.43 km. Again, negative means left. So the components of displacement to the east are negatve (-6.43 km). 3) First draw a vector diagram forces. Basically, draw a triangle ABC (not to scale – but if something may seem to the actual proportions would be better). Let AB = the force of 100 N (point the direction from A to B). then BC is the force of 80 N CA is the resultant vector (only) strength. Extend AB (like a flash and put a point D on the extension) CBD at an angle is 60 degrees. (For the angle ACB = 180-60 = 120 degrees) Now using the cosine law (which is: c ² = a ² + b ² – 2ab * cos (θ) where c is the length of the side you want to find (two sides are 80 and 100 N, so c is the remaining part), A and B are the two sides (80 and 100), and θ is the angle between A and B (between 80 and 100 vectors N). Solving for c, we obtain the magnitude of the resultant force. All that is needed is the address, which can be found either by the search for the two unknown angles. You will require sine law: sin (A) / a = sin (B) / b = sin (C) / c So where is the side opposite angle A, b is the side opposite B, etc. (4) Draw out again, its gonna be a right triangle. Draw a vector from 7 units up and continue from there another vector ranging from four units to the left (wind speed), plug the original vector (the tail of it) to the end of the second vector. You should have a right triangle with legs of 7 and 4, you can find the hypotenuse, and the angles by trigonometry. Sorry for being verbose and pointless. Its night and I'm very tired … In fact I accident now ….

sledding in west Iowa after Christmas Blizzard ’09