Question

initially object one is 100g and moving 1.5 m/s and object two is 180g. the velocity after the collision of the combined mass is .28m/s. what was the initial velocity of object 2.

Answer 1

Using the conservation of momentum, the initial velocity of object two before the collision is calculated to be -0.398 m/s, indicating it was moving in the opposite direction to object one.

Step-by-step explanation:

We are given an inelastic collision problem involving two objects. The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision, provided no external forces are acting on the system.

The formula for momentum is p = mv, where m is mass and v is velocity.

Let's denote the initial velocity of object two as u₂.

Using the conservation of momentum: (mass of object one) * (initial velocity of object one) + (mass of object two) * (u₂) = (combined mass of both objects) * (final velocity after collision)

Substituting given values and solving for u₂:

100g * 1.5 m/s + 180g * u₂ = 280g * 0.28 m/s
Converting grams to kilograms (since 1g = 0.001kg) and solving:

0.100kg * 1.5 m/s + 0.180kg * u₂ = 0.280kg * 0.28 m/s
0.150 kg⋅m/s + 0.180kg * u₂ = 0.0784 kg⋅m/s
Now, isolate u₂ and solve:

0.180kg * u₂ = 0.0784 kg⋅m/s - 0.150 kg⋅m/s
u₂ = (0.0784 kg⋅m/s - 0.150 kg⋅m/s) / 0.180kg
u₂ = -0.398 m/s (negative sign indicates opposite direction to object one)
This calculation gives us the initial velocity of object two before the collision.