A ball with a mass of #1 kg # and velocity of #4 m/s# collides with a second ball with a mass of #5 kg# and velocity of #- 7 m/s#. If #20%# of the kinetic energy is lost, what are the final velocities of the balls?

1 Answer
Nov 2, 2016

#v_1 = sqrt12.8 m/s#
#v_2 =2 sqrt7 m/s#

Explanation:

Let velocities of two balls after collision be # v_1 and v_2.#

For ball with mass 1 kg,
Kinetic Energy before collision# =1/2 mv^2#
Kinetic Energy before collision# =1/2 xx 1xx16 #
Kinetic Energy before collision# =8 J #
Kinetic Energy after collision# =8- 8xx20/100 #
Kinetic Energy after collision# =6.4 #
So, #1/2 xx 1 xx (v_1)^2 = 6.4#
#(v_1)^2 = 12.8#
#v_1 = sqrt12.8 m/s#

For ball with mass 5 kg,
Kinetic Energy before collision# =1/2 mv^2#
Kinetic Energy before collision# =1/2 xx 5xx-7 #
Kinetic Energy before collision# =-17.5 J #
Kinetic Energy after collision# =-17.5+ 17.5xx20/100 #
Kinetic Energy after collision# =-14 #
So, #1/2 xx 1 xx (v_2)^2 = -14#
#v_2 = sqrt28#
#v_2 =2 sqrt7 m/s#