A body of 1 kg carries a speed of = 40i. It is fragmented into Two pieces. If one, of 0.6 kg comes out with v1 = 200 i - 160 j; in m/s, How fast does the other one come out?

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 objects with masses mį = 2kg and m2 = 4kg collide and stick together as shown in the figure. The speed of m2 before the collision is V2i = 1.5m/s. The speed of the compound object after the collision is vf = 2m/s. Find the speed of m1 before the collision. m Vi m1 + m2 Before After Select one: O a. Vii = 9m/s O b. vii = 4m/s O c. Vii = 2m/s d. Vii = 10m/s O e. Vii = 8m/s

A 1400 kg weather rocket accelerates upward at 10 m/s^2. It explodes 1.6 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 590 m. What was the speed of the heavier fragment just after the explosion?