A ball with a mass of #5 kg # and velocity of #2 m/s# collides with a second ball with a mass of #6 kg# and velocity of #- 3 m/s#. If #75%# of the kinetic energy is lost, what are the final velocities of the balls?
1 Answer
-
Final velocity of the
#5color(white)(l)"kg ball:" -1.94color(white)(l)"m"*"s"^(-1)# -
Final velocity of the
#6color(white)(l)"kg ball:"-1.70color(white)(l)"m"*"s"^(-1)#
Explanation:
Let the final velocity be
Momentum conserves, hence
Construct a system of equations
Substitute
#v_1# in (1) with an expression of#v_2# derived from the first equation,#v_1=-1/5*(8+6*v_2)#
#5/2*(-1/5*(8+6*v_2))^2+3*v_2^2=37/4#
#132*v_2+192*v_2-57=0#
Correspondingly,
The first scenario is not possible since the one ball won't be able to overtake another in a collision in one-dimensional motions.
Therefore