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1. Consider a variable force F(x) that moves an object of mass m from point A (at xi) to point B (at xf). Derive the work-kinetic energy theorem, W = Ky - Ki [5] 2. A 5.20 g bullet moving at 672 m/s strikes a 700 g wooden block at rest on a frictionless surface. The bullet emerges, traveling in the same direction with its speed reduced to 428 m/s. What is the resulting speed of the block? [51 5 3. A 140 g ball with speed 7.8 m/s strikes a wall perpendicularly and rebounds in the opposite direction with the same speed. The collision lasts 3.80 ms. What are the magnitudes of the (a) impulse and [5] (b) average force on the wall from the ball? [5] 4. Three particles are located as shown in the figure below, with masses m =3.0 kg, m2 = 4.0 kg. and m3 = 8.0 kg. The scales on the axes are set by Xs = 2.0 m and ys = 2.0 m. y (m) m3 Is m2 mi x (m) 0 (a) What is the x-coordinate of the system's centre of mass? (b) What is the y-coordinate of the system's centre of mass? [5 [5)