A ball with a mass of #5 kg# moving at #3 m/s# hits a still ball with a mass of #8 kg#. If the first ball stops moving, how fast is the second ball moving?

Answer 1

#v_(2f)~~2"m"//"s"#

We can calculate the final velocity of the second ball using momentum conservation. Momentum is conserved in all collisions.

In an inelastic collision, momentum is conserved as always, but energy is not; part of the kinetic energy is transformed into some other form of energy. Therefore, we have an inelastic collision.

#color(skyblue)(vecp=mvecv)#
The equation for momentum, where #m# is the mass of the object and #v# is the object's velocity.

Momentum conservation:

#DeltavecP=0#
#=>vecp_f=vecp_i#

For multiple objects, we use superposition as with forces:

#vecP=vecp_(t o t)=sumvecp=vecp_1+vecp_2+...+vecp_n#

So we have:

#=>color(crimson)(m_1v_(1i)+m_2v_(2i)=m_1v_(1f)+m_2v_(2f))#

We are given the following information:

Factoring in our zero values, we now have:

#m_1v_(1i)+cancel(m_2v_(2i))=cancel(m_1v_(1f))+m_2v_(2f)#
#=>m_1v_(1i)=m_2v_(2f)#
Which we can solve for #v_(2f)#:
#color(darkgray)(v_(2f)=(m_1v_(1i))/m_2)#

Substituting in our known values:

#v_(2f)=((5"kg")(3"m"//"s"))/(8"kg")#
#=1.875"m"//"s"#
#~~color(darkblue)(2"m"//"s")#

This answer can be checked by comparing the momentum before and after the collision. They should both be equal by momentum conservation.

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Answer 2

The second ball will be moving at 1.2 m/s in the opposite direction.

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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.

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.

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.

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.

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