A ball with a mass of #9 kg # and velocity of #2 m/s# collides with a second ball with a mass of #3 kg# and velocity of #- 5 m/s#. If #10%# of the kinetic energy is lost, what are the final velocities of the balls?

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Answer 1 · 2018-07-29T18:59:58

The solution is #=((-1.41, 5.23))ms^-1#

#m_1u_1+m_2u_2=m_1x+m_2y#

Plugging in the above values

#9*2+3*-5=9x+3y#

#9x+3y=18-15=3#

#3x+y=1#.................................#(1)#

#10%# of kinetic energy is lost

#(1/2m_1u_1^2+1/2m_2u_2^2)*9/10=1/2m_1x^2+1/2m_2y^2#

Plugging the data

#(9*2^2+3*5^2)*9/10=9x^2+3y^2#

#9x^2+3y^2=99.9#

#3x^2+y^2=33.3#......................................#(2)#

Solving equations #(1)# and #(2)# graphically

graph{(3x+y-1)(3x^2+y^2-33.3)=0 [-18.02, 18.03, -9.01, 9.01]}

The solutions are #=(-1.41, 5.23)# or #=(1.91, -4.73)#

The second solution is discarded