A ball with a mass of #7 kg # and velocity of #1 m/s# collides with a second ball with a mass of #6 kg# and velocity of #- 5 m/s#. If #75%# of the kinetic energy is lost, what are the final velocities of the balls?

Answer 1

The final velocity is #=1.74 ms^(-1)#

Kinetic Energy #=1/2mv^2# KE of first ball #=1/2*7*1^2=3.5J# KE of second ball #=1/2*6*25=75J# Total KE before collision #=78.5J# Energy remaining after collision #=25/100*78.5=19.625J# Total mass #=13 kg# #E=1/2mv^2##=>##19.625=1/2*13*v^2# So #v^2=(19.625*2/13)# Final velocity #sqrt(19.625*2/13)=1.74 ms^(-1)#

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Answer 2

Sebastian Acosta

To find the final velocities of the balls, you can use the conservation of momentum and the fact that 75% of the kinetic energy is lost during the collision. First, calculate the initial momentum of the system using the masses and velocities of the balls. Then, use the fact that momentum is conserved during the collision. Finally, use the conservation of kinetic energy to find the final velocities of the balls.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.