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A 0.017 g coin sliding to the right at 0.255 m/s makes an elastic head-on collision with a 0.040 g coin that is initially at rest. After the collision, the 0.017 g coin moves to the left at 0.108 m/s. Find the final velocity of the other coin.

Answer :

Corsaquix

Answer:

[tex]\approx 0.154\:\mathrm{m/s}[/tex]

Explanation:

In all collisions, whether elastic or inelastic, momentum must be conserved. Therefore, we can write an equation using the conservation of momentum:

[tex]m_{c1}v_{c1,i}+m_{c2}v_{c2,i}=m_{c1}v_{c1,f}+m_{c2}v_{c2,f}[/tex]

Solving for [tex]v_{2c,f}[/tex]:

[tex]0.000017\cdot 0.255+0.000040\cdot0=0.000017\cdot (-0.108)+0.000040\cdot v_{c2,f},\\v_{c2,f}\approx \boxed{0.154\:\mathrm{m/s}}[/tex]

*Notes:

-It's important to convert g to kg, as kg is the SI unit of mass

-The negative sign in a velocity measure represents direction

-Since the velocity we solved for is positive, it implies that the direction is to the right

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