When an object at rest explodes into two part fly apart must they move in exactly opposite directions(b) when a moving object strikes a stationary one must they move off in exactly opposite directions?

Answer 1

Very few questions are this much challenging to answer! The answer is no. Both parts can move in any direction including the opposite direction. The final outcome will depend upon the amount of energy released by the explosion. The amount of energy taken in by the breakage of the object. ( The rest of the energy will be taken up by the two objects to move away from each other.) Whether the explosion takes place at the center of gravity or away from it. When explosion takes place at the center of gravity, two parts will be driven away from each other. If the explosion takes place away from the center of gravity, then the whole piece will together move away from the explosion point in opposite direction of the explosion point. The final direction of the two parts will be decided by the center of the gravity of the both parts. There are very less chances that both the parts will move in opposite direction. In most of the cases both parts will move away from each other making an angle. The bigger part will move away with less speed. It can be further explained with the help of the diagram and trignomentry. In day today life you have got a gun. Here in explosion takes place inside the barrel. It seems that the bullet and the gun move in opposite direction. It is true. But the direction is not exactly opposite. It is roughly opposite. Here the bullet takes a high speed. Because it has got a less mass. The gun also gets a recoil. As you can feel the thrust in case of rifle on your shoulder. When both the parts move away in opposite direction, the product of mass and velocity is same. Now the second question is very easy to answer. You see that in day to day game of carrom board or the billiard. Here you strike at the periphery of the ball and both of them move away by making an angle. Here also the angular momentum plays a role.

Answer 2

In an explosion, the two parts can move in opposite directions, but they do not have to move exactly in opposite directions. The direction of each part's motion depends on the distribution of internal forces during the explosion. Similarly, when a moving object strikes a stationary one, they do not have to move off in exactly opposite directions. The resulting motion depends on the properties of the objects involved and the collision itself.