If a thrown object strikes an obstacle and bounces back with the same velocity in the opposite direction, the change in momentum of the object can be calculated using the principle of conservation of momentum.
The momentum of an object is given by the product of its mass (m) and velocity (v). Let's assume the initial momentum of the object before the collision is P₁ and the final momentum after the collision is P₂.
Initially, the momentum is in one direction (let's say positive direction), and after the collision, the momentum is in the opposite direction (negative direction). So, the change in momentum (ΔP) is the difference between the final and initial momentum.
ΔP = P₂ - P₁
Since the object bounces back with the same velocity in the opposite direction, the final velocity (v₂) will be the negative of the initial velocity (v₁).
P₁ = m * v₁ P₂ = m * v₂
But v₂ = -v₁ (opposite direction)
Therefore, P₂ = m * (-v₁) P₂ = -m * v₁
Substituting these values into the equation for the change in momentum:
ΔP = (-m * v₁) - (m * v₁) ΔP = -2m * v₁
So, the change in momentum of the object is equal to -2 times the initial momentum (assuming the masses remain constant). The negative sign indicates a change in direction, reflecting the fact that the object bounces back with the opposite velocity.