1. If two collinear vectors A and B are added, the resultant has a magnitude equal to 4.0. If vector B is subtracted from vector A the resultant has a magnitude equal to 8.0. What is the magnitude of vector A?

2. Given that vector A + 2 B=x1i+y1j and 2A-B-x2i+y2j. What is A?

The answer is (1/5)(x1+2x2)i+(1/5)(y1+2y2)j. Why?

3. A Ferris wheel rotates five times each minute and carries each car around a circle of diameter 18.0m.

What force (magnitude and direction) does the seat exert on a 38.0 kg child when the rider is halfway between top and bottom(on the way down):


Direction (angle measured inward from the vertical)?


At = 0, a particle is located at x = 25 m and has a velocity of 15 m/s in positive x dirction. The acceleration of the particle varies with time as shown in the diagram. What is the velocity of the particle at t = 5.0s? The anwer is
+30 m/s but how?

Could you explain the answers in detalis? Thanks a lot.