Please help with the following Vector Questions.

1 . Fig. 1.1 shows three forces acting on a particle at O. Find the magnitude and direction of the resultant force acting on the particle.(Ans: 3.15 N, 49 below -ve x-axis) AN - X 30" 65. & N +6N Fig. 1.1 2. A woman is driving her car due North at a speed of 22 m s". To take a curve on the highway, she reduces the speed of the car to 20 m s" and turn the car 30" East of North. Calculate the magnitude and direction of the change in the velocity of the car. (Ans: 1 1 m s', 25 below +ve x-axis) 3. A 400 N box is supported by light ropes as shown in Fig. 3.1. Find the tensions labeled T and T, in the two ropes shown. (Ans: T, = 354 N, T, = 434 N) 20" Fig. 3.1 72 400 N4. One end of a uniform beam of weight 500 N and length 3 m rests on the ground, the other end is held above the ground by the pivot placed I'm from the other end as shown in Fig. 4.1. An 800 N man walks along the beam, from the lower end towards the higher end. How far from the pivot can the man walk before the high end of the beam swings down? (Ans: 0.31 m) 2 m Fig. 4.15. A uniform beam weighing 2000 N is held in a horizontal position by means of a hinge at one end and a light cable fastened to the other end as shown in Fig. 5.1. The cable makes a 20" angle with the beam. Calculate cable 20" hinge Fig. 5.1 (i) the tension in the cable. (Ans: 2924 N) (ii) the horizontal and vertical components of the force at the hinge. (H = 2748N and V = 1000 N) (iii) the magnitude and direction of the resultant force at the hinge. ( R = 2924 N, 0 = 20")