Answer:
The final velocity of the 15.0-kg object after the collision is 2.47 m/s in forward direction.
Explanation:
Given;
mass of the object, m₁ = 15 kg
initial velocity of this object, u₁ = 0
mass of the second object, m₂ = 10.5 kg
initial velocity of this object, u₂ = 3.0 m/s
let the final velocity of the first object = v₁
also, let the final velocity of the second object = v₂
Apply the principle of conservation of linear momentum
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
(15 x 0) + (10.5 x 3) = 15v₁ + 10.5v₂
31.5 = 15v₁ + 10.5v₂ ----- (1)
One directional velocity;
u₁ + v₁ = u₂ + v₂
0 + v₁ = 3 + v₂
v₂ = v₁ - 3 ------(2)
Substitute (2) into (1);
31.5 = 15v₁ + 10.5v₂
31.5 = 15v₁ + 10.5(v₁ - 3)
31.5 = 15v₁ + 10.5v₁ - 31.5
63 = 25.5v₁
v₁ = 63 / 25.5
v₁ = 2.47 m/s
Therefore, the final velocity of the 15.0-kg object after the collision is 2.47 m/s in forward direction.
