Vectors and resultant force

Question

1. Two ships start from the same point, one travelling 24 knots E and the other 18 knots N. What is their vector difference (resultant)?
2. Two forces of 10 N each acting on a point, one force acts East and the other 70^o N of E. Find the resultant force.
3. Add the following vectors: A = 10N, 70^o S of E; B = 5 N, E; C = 15 N, NE and D = 15N 60^o N of W.

Answer 1

Hi Leah Anne

1) This question uses the right triangle theorem. The vector difference is the distance between the end points of the two vectors. If you draw the two velocity vectors, you have one at 24 East and one at 18 north. Connecting the two end points is a vector (let's go from East to North) the resultant is a vector headed somewhat Northwest. The magnitude is the square root of 24 squared + 18 squared which is 30 (it's a 3-4-5 triangle. The angle is the arctan of 18/24 or 37 degrees west of north

2) For this problem, you add the vectors together. To add them you add the components. The force at 70 degree N of E has components of 10sin70 N and 10cos70 E. Sun the N and E components, and use the results to compute the resultant like we did in Problem 1.

3) This one works best if you draw the vectors on a graph. Add all the sines together and do the came for the cosines. The resultant components give you both the magnitude and the angle using the steps of problem 1