Object A moving due east collides with object B moving due w

Object A moving due east collides with object B moving due west. After the collision, A is moving 20 degree north of due east. What must be true of B after the collision? B must be moving 20 degree south of due east. B must be moving 20 degree south of due west. At least part of B\'s velocity must be toward the west. At least part of B\'s velocity must be toward the south. None of these.

Solution

by the conservation of moentum ,

              m_av_a + m_b v_b = m_a v´_a + m_b v´_b

m_{a ,} m_b be the masses of objects A and B respectively

v_a , v_b are the intial velocitys and   v´_a , v´_b be the velocitys after collision

since the intial velocitys of the two objects are just pointing east and west direction imagin along postive x - axis is east and negative x-axis is west ,

before collision there is no meomentum along y-direction , i.e along perpendicular direction to x-axis

after the collision Object A is making an angle 20 towards north due east bringing some velocity component along yaxis as shown in the figure

so by conservation of moemtum along y axis , object B should possess velocity component projected on y axis along south , and the angle of B depends on the mass ratios of A and B .

so the answer is D. at least part of B´s velocity must be south

                                      applying conservation of momentum after collision along yaxis

                                      m_av_a + m_b v_b = m_a v´_a + m_b v´_b

                                      _{0         +        0    =}   m_a v´_a cos (20) + m_b v´_b cos (x)

            m_a v´_a cos (20) = - m_b v´_bcos (x) (shown in green in the diagram)

v´_a cos (20) shown in red arrow and v´_bcos (x) shown in green in the diagram

           angle x depends on m_a and m_b.