Please label each question

Mechanics - PHYS 211 Homework 9 Problem 1: An .M = 20 kg wood ball hangs from an R = 2.0m long wire. The maximum tension the wire can withstand without breaking is Tum = 400 N. An in = 1.0 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the greatest speed. Up. this projectile can have without causing the wire to break? a) From the conservation of momentum, nd the formula for the speed c of the system ball+projectile immediately after the collision as a function of up. in and M. FIG. 1: The scheme for Problem 1 b) After the collision, the system becomes a pendulum with mass [m + M) shown in Fig. 1. Initially, when the wire is vertical, the ball has a centripetal acceleration fir (so, T has to be larger in magnitude than [in + M )5), while the tangential acceleration E, is zero. When the wire is at a maximum angle 9 from the vertical. or = 0, the radial components of the (smaller) tension f and (m + M) cancel each other. while the tangential component of {in + Mir} creates the tangential acceleration. This scheme is meant to illustrate that the tension in the wire will be the highest immediately after the collision, when the wire is still vertical, not at a later moment of time. Writing down Newton's second law for the pendulum immediately after the collision, and using the speed a from the previous step to compute the centripetal acceleration, show that the greatest speed that the projectile can have without causing the wire to break is given by the formula 0;, = \"1:" 1f 139;? gR. c) Compute the numerical value of op