A ball of mass 200g, travelling with a velocity of 100m/s, collides with another ball of mass 800g, moving at 50m/s in thesame direction. If they stick togdther, what will be their common velocity?

Using inelastic collision formula:

m1u1 +m2u2 = (m1+m2)V
(200*100) + (800*50) = ( 200+800)V
20000+40000 = 1000V
60000 = 1000V
V = 60000 / 1000
V = 60

conservation of momentum applies.

initial momentum=final momentum
200*100+800*50=(200+800)Vf solve for Vf, in m/s

A ball of mass 200g, travelling with a velocity of 100m/s, collides with another ball of mass 800g, moving at 50m/s in thesame direction. If they stick togdther, what will be their common velocity?

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Ok

Momentum before impulse= momentum after impulse

(0.2×100)+(0.8×50)=(0.2+0.8)v
where v is the common velocity.
(20+40)=1v
60=v
v=60
therefore, the common velocity is 60m/s

To find the common velocity of the two balls after they stick together, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is given by the product of its mass and velocity. So, the momentum before the collision is:

Momentum before collision = (mass of first ball) * (velocity of first ball) + (mass of second ball) * (velocity of second ball)

P₁ = (m₁ * v₁) + (m₂ * v₂)

where:
m₁ = mass of first ball = 200g = 0.2 kg
v₁ = velocity of first ball = 100m/s
m₂ = mass of second ball = 800g = 0.8 kg
v₂ = velocity of second ball = 50m/s

Plugging in these values:

P₁ = (0.2 kg * 100m/s) + (0.8 kg * 50m/s)
= 20 kg·m/s + 40 kg·m/s
= 60 kg·m/s

The total momentum after the collision will be the same as the total momentum before the collision. Since the balls stick together, their masses combine, and we can represent their combined mass as the sum of their individual masses (m₁ + m₂ = 0.2 kg + 0.8 kg = 1 kg).

Now, let's assume the common velocity of the two balls after the collision is v₃.

So, momentum after collision = (mass of combined balls) * (common velocity after collision)

P₂ = (m₁ + m₂) * v₃

Plugging in the values:

P₂ = 1 kg * v₃

Since the total momentum is conserved, we have:

P₁ = P₂
60 kg·m/s = 1 kg * v₃

Simplifying, we get:

v₃ = 60 m/s

Therefore, the common velocity of the two balls after the collision is 60 m/s.