Q8, adm Q9

{8) [5 points] Find the center of mass of a cone of length L and base radius R. Approach: find the mass of a thin slice aim at distance x from the tip. Integrate over all such masses from 0 to it. You will also need the total mass M, which you can find1 from the volume mass density p times the volume of a cone, which is V = Tfth/B. (9) [5 points] A fireworks shell reaches the top of its trajectory (and is therefore briefly at rest) when it bursts into three pieces, all moving in the x - 3/ plane. One piece, of mass m, moves sideways with velocity {+30 m/s) 1 and a second piece, also of mass m, moves upward with velocity (+30 m/s)f. The third piece has mass 3m. (3) Find the velocity vector components of the third piece and calculate the magnitude of the velocity. (b) Draw the three vectors to scale in a coordinate system with the shell at the center (Le. on graph paper or quadrille background). (c) Now calculate and draw the three velocity vectors if the shell burst while traveling upwards (in the +1\" direction) at 60 m/s. Hint: just transform the velocity vectors to the moving frame of reference. 1 You can find it yourself by the same methods you are using to find Xm