(Solved): A shell is shot with an initial velocity \( \vec{v}_{0} \) of \( 15 \mathrm{~m} / \mathrm{s} \), at ...

A shell is shot with an initial velocity \( \vec{v}_{0} \) of \( 15 \mathrm{~m} / \mathrm{s} \), at an angle of \( \theta_{0}=63^{\circ} \) with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass (see the figure). One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming that the terrain is level and that air drag is negligible? Number Units A body of mass \( 3.1 \mathrm{~kg} \) makes an elastic collision with another body at rest and continues to move in the original direction but with \( 1 / 2 \) of its original speed. (a) What is the mass of the other body? (b) What is the speed of the two-body center of mass if the initial speed of the \( 3.1 \mathrm{~kg} \) body was \( 8.6 \mathrm{~m} / \mathrm{s} \) ? (a) Number Units (b) Number Units A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of \( 73.2 \times 10^{5} \mathrm{~kg} \), of which \( 16.2 \times 10^{5} \mathrm{~kg} \) is fuel. The rocket engine is then fired for \( 380 \mathrm{~s} \), during which fuel is consumed at the rate of \( 360 \mathrm{~kg} / \mathrm{s} \). The speed of the exhaust products relative to the rocket is \( 4.33 \mathrm{~km} / \mathrm{s} \). (a) What is the rocket's thrust? After the 380 s firing. what are (b) the mass and \( (\mathrm{c}) \) the speed of the rocket? (a) Number Units (b) Number Units (c) Number Units Particle 1 of mass \( 327 \mathrm{~g} \) and speed \( 3.68 \mathrm{~m} / \mathrm{s} \) undergoes a one-dimensional collision with stati?nary particle 2 of mass \( 322 \mathrm{~g} \). What is the magnitude of the impulse on particle 1 if the collision is (a) elastic and (b) completely inelastic? (a) Number Units (b) Number Units