question_answer 50)

                  A bullet of mass m fired at \[{{30}^{o}}\] to the horizontal leaves the barrel of the gun with a velocity \[\upsilon \]. The bullet hits a soft target at a height h above the ground while it is moving downward and emerges out with half the kinetic energy it had before hitting the target. Which of the following statements are correct in respect of bullet after it emerges out of the target?                 (a) The velocity of the bullet will be reduced to half its initial value.                 (b) The velocity of the bullet will be more than half of its earlier velocity.                 (c) The bullet will continue to move along the same parabolic path.                 The bullet will move in a different parabolic path.                 (e) The bullet will fall vertically downward after hitting the target.                 (f) The internal energy of the particles of the target will increase.                

Answer:

                  (b, d, f) Horizontal component of \[\upsilon \,=\upsilon \,\cos \,{{30}^{o}}\] remains constant throughout the journey of the projectile. The vertical component of \[\upsilon \,=\upsilon \,\sin \,{{30}^{o}}\] decreases after projection and becomes zero at the highest point. Then projectile begins to fall downwards and vertical component goes on increasing. When bullet hits the soft target, part of K.E. of bullet is transferred to the target. Hence internal energy of the target increases. Target continues to move along the same parabolic path if only force of gravity acts on it.