(b) Given that the he the equation for u(t) , including num e positive direction for all quantities is to the Is attached to one end of a horizontal spri Ition of the block as it oscillates. The resultin- pring and releasing the block from rest at tim of the spring is attached to a fixed wall. The block is Time /(s) 9. A motion city u vers Collisions 10. A bullet of mass 10 g strikes a ballistic pendulum of mass 2.0 kg. The center of mass of the pendulum rises a vertical distance of 12 cm. Assuming that the bullet remains embedded in the pendulum, calculate its initial speed. values 12 cm 2.0 kg 11. A 5.0 kg particle with a velocity of 3.0 m/s collides with a 10 kg particle that has a velocity of 2.0 m/s in the same direction. After the collision, the 10 kg particle is observed to be traveling in the original direction with a speed of 4.0 m/s. (a) Calculate the velocity of the 5.0 kg particle immediately after the collision. (b) By how much does the total kinetic energy of the system of two particles change because of the collision? (c) How might you account for your answer in b)? 12. Two particles, one having twice the mass of the other, are held together with a compressed spring between them. The energy stored in the spring is 60 J. How much kinetic energy does each particle have after they are released? Assume that all stored energy is transferred to the particles and that neither particle is attached to the spring after they are released. 13. A 35 ton railroad freight car collides with a stationary caboose car. They couple together and 27% of the initial kinetic energy is dissipated as heat, sound, vibrations, and so on. Find the weight of the caboose. 14 . An alpha particle collides with an oxygen nucleus, initially at rest. The particle is scattered at an angle of 64 above its initial direction of motion and the oxygen nucleus recoils at an angle of 510 below this initial direction. The final speed of the nucleus is 1.2 x 10 m/s. Calculate the final speed of the particle. (The mass of an alpha particle is 4.0 u and the mass of an oxygen nucleus is 16 u.) 15. Two vehicles A and B are traveling west and south, respectively, toward the same intersection where they collide and lock together. Before the collision, A (total weight 2700 lb.) is moving with a speed of 40 mi/h and B (total weight 3600 lb.) has a speed of 60 mi/h. Find the magnitude and direction of the velocity of the (interlocked) vehicles immediately after the collision