Question 1: A man exerts a 60-lb force F to push a crate onto a truck. (a) Express F in terms of components using the coordinate system shown. (b) The weight of the crate is 100 lb. Determine the magnitude of the sum of the forces exerted by the man and the crate's weight.

Question 2: The x and y coordinates of points A, B, and C of the sailboat is shown.

(a) Determine the components of a unit vector that is parallel to the forestay AB and points from A toward B.

(b) Determine the components of a unit vector that is parallel to the backstay BC and points from C toward B.

Question 3: (a) The magnitudes of the forces exerted by the cables are |T₁| = 2800 lb, |T₂| = 3200 lb, |T₃| = 4000 lb, and |T₄| = 5000 lb. What is the magnitude of the total force exerted by the four cables?

(b) The tensions in the four cables are equal: |T₁| = |T₂| = |T₃| = |T₄| = T. Determine the value of T so that the four cables exert a total force of 12,500-lb magnitude on the support.

Question 4:  Four groups engage in a tug-of-war. The magnitudes of the forces exerted by groups B, C, and D are |F_B| = 800 lb, |F_C| = 1000 lb. |F_D| = 900 lb. If the vector sum of the four forces equals zero, what are the magnitude of F_A and the angle α?