Answer:
Common velocity will be 2 m/sec
Explanation:
We have given a car of mass 1000 kg is traveling in east at 20 m /sec
So [tex]m_1=1000kg[/tex] and [tex]v_1=20m/sec[/tex] ( take east direction as positive )
And another car of mass 1500 kg is moving with 10 m/sec in west direction
So [tex]m_1=1500kg[/tex] and [tex]v_2=-10m/sec[/tex] ( west direction will be negative direction )
According to law of conservation of momentum
[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]
[tex]1000\times 20-1500\times 10=(1000+1500)v[/tex]
[tex]v=\frac{5000}{2500}=2m/sec[/tex]
So common velocity will be 2 m/sec
The common velocity of the cars after the collision is 2m/s
According to the law of collision, the sum of momentum before the collision is equal to the sum of momentum after the collision. Mathematically;
[tex]m_1u_1+m_2u_2=(m_1+m_2)v[/tex]
Substitute the given parameters into the formula
v is the common velocity of the cars after the collision
[tex]1000(20) + 1500(-10) = (1000+1500)v\\20,000 - 15,000 = 2500v\\5000 = 2500v\\v = 5000/2500\\v = 2m/s\\[/tex]
Hence the common velocity of the cars after the collision is 2m/s
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