Question

An object of mass 3.05 kg, moving with an initial velocity of 4.90 i hat m/s, collides with and sticks to an object of mass 2.01 kg with an initial velocity of -3.62 j hat m/s. Find the final velocity of the composite object.

v=(......i+.....j)

Answer 1

initail momentum along x direction =MV_x

                                                                =3.05*4.90 kg m/s

                                                                =14.945 i kg m/s

and momentum along y direction = MV_y

                                                             =2.01*(-3.62) j kg m/s

                                                             = -7.2762 j kg m/s

final mass of system=M₁+M₂

                                     =3.05+2.01

                                      =5.06 kg

conserving momentum along x direction

final momentum =initial momentum

14.945 i kg m/s=M_f V_X

                        =5.06 kg * Vx

so velocity along x is V_x =14.945/5.06

                                      =2.953 i m/s

again

conserving momentum along y direction

final momentum =initial momentum

-7.2762 j kg m/s=M_f Vy

                        =5.06 kg * Vy

so velocity along x is Vy =-7.2762 /5.06

                                       = -1.4379 j m/s

v=(2.953 i-1.4379j)