Subject: Physics Caption: This question already has an answer, but I am in need of a more detailed and handwritten solution.

2.16 A loaded spring gun, initially at rest on a horizontal frictionless surface, fires a marble at an angle of elvation 0 . The mass of the gun is M, the mass of the marble is m, and the muzzle velocity of the marble is v.. Find the final motion of the gun. Solution: The final motion of the gun can be found easily by using conservation of momentum. If air resistance is negligible, then there are no horizontal external forces acting on the sys- tem (the gun and marble), and the x component of the equation of motion F = dP / dt is 0 = - dP dt hence P, is conserved: Pxinitial = Px, find Since the system is initially at rest, so Printfial = 0. - V. CosB- V. It is apparent that P. is not zero. We now come to find out what it is. v. is the velocity of the marble Fig. 2.1 6 relative to the gun, not to the table. As shown in Fig. 2. 16, the horizontal speed of the marble relative to the table is v. coso - V .So we have 0= m(v. cos 0 - V.) - MV my cose or V. = m + M