A ball with a mass of # 2 kg# is rolling at #5 m/s# and elastically collides with a resting ball with a mass of #9 kg#. What are the post-collision velocities of the balls?

Answer 1

#=>u=5/3ms^-1# and #v=20/27ms^-1#

If post collision velocities be u m/s for 1st one and v m/s for 2nd one ,then applying conservation of momentum #uxx2+vxx9=2xx5+0xx9# #=>uxx2+vxx9=10# #=>vxx9=10-uxx2# #=>vxx9=(5-u)xx2 .......(1)#

Now collision being elastic KE will be conserved and consequently the relative velocity of 1st object with respect to 2nd is reversed . So #1/2xx2xx5^2+1/2xx9xx0^2=1/2xx2xxu^2+1/2xx9v^2# #=>2xx5^2=2xxu^2+9v^2# #=>2xx5^2-2xxu^2=9v^2# #=>2xx(5^2-u^2)=9v^2# #=>2xx(5+u)(5-u)=9v^2# #=>(5+u)9v=9v^2# #=>(5+u)=9v......(2)# #[:.v!=0]# Comparing (1) and (2) #5+u=10-2u# #=>3u=10-5# #=>u=5/3ms^-1# and #v=20/27ms^-1#

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Answer 2

Emily Abbate

Using the principles of conservation of momentum and kinetic energy, we can calculate the post-collision velocities of the balls. The velocity of the 2 kg ball after the collision will be approximately 1.11 m/s, and the velocity of the 9 kg ball will be approximately 3.89 m/s.

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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.