a 9.0 kg cannonball is flying 21.6m/s (E) when it explodes into two fragments. One 3.2kg fragment goes off at 10.3m/s (45degrees S of E). What will be the magnitude of the velocity of the second fragment immediately after the explosion? Assume no mass is lost during the explosion.
Original x momentum = 9 *21.6 = 194.4 kg m/s
Original y momentum = 0
Final x momentum = 3.2 * 10.3 * cos 45 + (9-3.2) Vx
Final y momentum = -3.2 * 10.3 * sin 45 + (9-3.2) Vy
momentum is conserved
so
194. 4 = 23.3 + 5.8 Vx
0 = -23.3 + 5.8 Vy
solve for Vx and Vy
magnitude = sqrt (Vx^2 + Vy^2)