= (10%) Problem 8: A baseball of mass m₁ = 0.36 kg is thrown at another ball hanging from the ceiling by a long string. The second ball m2 0.89 kg is initially at rest while the baseball has an initial horizontal velocity of V₁ = 6.9 m/s. After the collision the first baseball falls straight down (no horizontal velocity). @theexpertta.com - tracking id: 6C65-C5-6B-4E-822C-46694. In accordance with Expert TA's Terms of Service. copying this information to any solutions sharing website is strictly forbidden. Doing so may result in termination of your Expert TA Account. 50% Part (a) How fast, in m/s, is the second ball moving immediately after the collision? v = || 9 HOME 85 63 () EN * 7 4 1 2 sin() cotan() atan() cosh() tanh() cos() asin() acos() acotan() sinh() tan() π cotanh() Degrees Radians + - 0 VO BACKSPACE END DEL CLEAR Ꮎ L V₁ Submit Hint Feedback I give up! Hints: 0 for a 0% deduction. Hints remaining: 0 Feedback: 0% deduction per feedback. m₁ m 2Otheexpertta.com 50% Part (b) How high, in m, does the ball swing upwards after the collision before it swings back down again? Grade Summary Deductions Potential Submissions 0% 100% Attempts remaining: 6 (4% per attempt) detailed view

Problems 44 and 45 are paired. C A model rocket is shot straight up. As it reaches the highest point in its trajectory, it explodes in midair into three pieces with velocities indicated by the arrows in Figure P10.44, as viewed from directly above the explosion. Rank the mass of each piece in order from smallest to largest and justify your answer. FIGURE P10.44 Problems 44 and 45.

Initially, ball 1 rests on an incline of height h, and ball 2 rests on an incline of height h/2 as shown in Figure P11.40. They are released from rest simultaneously and collide elastically in the trough of the track. If m2 = 4 m1, m1 = 0.045 kg, and h = 0.65 m, what is the velocity of each ball after the collision?

Review. A bullet of mass m = 8.00 g is fired into a block of mass M = 250 g that is initially at rest at the edge of a frictionless table of height h = 1.00 m (Fig. P9.45). The bullet remains in the block, and after the impact the block lands d = 2.00 m from the bottom of the table. Determine the initial speed of the bullet. Figure P9.45 Problems 45 and 46.

Initially, ball 1 rests on an incline of height h, and ball 2 rests on an incline of height h/2 as shown in Figure P11.40. They are released from rest simultaneously and collide in the trough of the track. If m2 = 4 m1 and the collision is elastic, find an expression for the velocity of each ball immediately after the collision. FIGURE P11.40 Problems 40 and 41.

A water molecule consists of an oxygen atom with two hydrogen atoms bound to it (Fig. P8.36). The angle between the two bonds is 106. If the bonds are 0.100 nm long, where is the center of mass of the molecule? Figure P8.36

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?

Two bumper cars at the county fair are sliding toward one another (Fig. P11.54). Initially, bumper car 1 is traveling to the east at 5.62 m/s, and bumper car 2 is traveling 60.0 south of west at 10.00 m/s. They collide and stick together, as the driver of one car reaches out and grabs hold of the other driver. The two bumper cars move off together after the collision, and friction is negligible between the cars and the ground. a. If the masses of bumper cars 1 and 2 are 596 kg and 625 kg respectively, what is the velocity of the bumper cars immediately after the collision? b. What is the kinetic energy lost in the collision? c. Compare your answers to part (b) from this and Problem 54. Is one answer larger than the other? Discuss and explain any differences you find.

(a) Figure P9.36 shows three points in the operation of the ballistic pendulum discussed in Example 9.6 (and shown in Fig. 9.10b). The projectile approaches the pendulum in Figure P9.36a. Figure P9.36b shows the situation just after the projectile is captured in the pendulum. In Figure P9.36c, the pendulum arm has swung upward and come to rest momentarily at a height A above its initial position. Prove that the ratio of the kinetic energy of the projectilependulum system immediately after the collision to the kinetic energy immediately before is m1|/(m1 + m2). (b) What is the ratio of the momentum of the system immediately after the collision to the momentum immediately before? (c) A student believes that such a large decrease in mechanical energy must be accompanied by at least a small decrease in momentum. How would you convince this student of the truth? Figure P9.36 Problem. 36 and 43. (a) A metal ball moves toward the pendulum. (b) The ball is captured by the pendulum. (c) The ballpendulum combination swings up through a height h before coming to rest.

A girl of mass mg is standing on a plank of mass mp. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity gp to the right relative to the plank. (The subscript gp denotes the girl relative to plank.) (a) What is the velocity pi of the plank relative to the surface of the ice? (b) What is the girls velocity it pi relative to the ice surface?