A 3kg object initially moving in the positive x-direction with a velocity of +5m/s collides with and sticks to a 2kg object initially moving in the negative y-direction with a velocity of -3m/s. Find the final components of velocity of the composite object.
Well, well, well, it seems we have a collision on our hands! Let's see what we can do here.
Since both objects collide and stick together, we can find the final components of velocity by using the principle of conservation of momentum.
The initial momentum in the x-direction is given by the equation: (mass1 * velocity1) + (mass2 * velocity2) = 0
Now, let's plug in the values: (3kg * 5m/s) + (2kg * -3m/s) = 0
That gives us: 15kg*m/s - 6kg*m/s = 0
Solving for the final momentum in the x-direction gives us: 9kg*m/s
Since the objects stick together, they have a combined mass of 3kg + 2kg = 5kg.
To find the final velocity in the x-direction, we divide the final x-momentum by the final mass: 9kg*m/s / 5kg = 1.8m/s
So, we can conclude that the final velocity of the composite object in the x-direction is +1.8m/s.
As for the y-direction, it's a bit of a clown show. Since the 2kg object was initially moving in the negative y-direction and sticks to the 3kg object, we can assume that the final velocity in the y-direction is just the initial velocity of the 2kg object. Therefore, the final velocity in the y-direction is -3m/s.
Hence, the final components of velocity for the composite object are +1.8m/s in the x-direction and -3m/s in the y-direction.
Hope that gives you a smile and clears things up!
To find the final components of velocity of the composite object, we can apply the law of conservation of momentum, which states that 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. Therefore, the momentum of the 3kg object before the collision is (3kg)(5m/s) = 15kg·m/s in the positive x-direction, and the momentum of the 2kg object before the collision is (2kg)(-3m/s) = -6kg·m/s in the negative y-direction.
Since the objects stick together after the collision, they have a combined mass of 3kg + 2kg = 5kg.
To find the final velocity of the composite object, we need to find the total momentum after the collision and divide it by the combined mass.
The total momentum after the collision in the x-direction is (15kg·m/s) + 0kg·m/s = 15kg·m/s.
The total momentum after the collision in the y-direction is 0kg·m/s + (-6kg·m/s) = -6kg·m/s.
The final velocity of the composite object in the x-direction is therefore (15kg·m/s) / (5kg) = 3m/s in the positive x-direction.
The final velocity of the composite object in the y-direction is (-6kg·m/s) / (5kg) = -1.2m/s in the negative y-direction.
Therefore, the final components of velocity of the composite object are:
Vx = 3m/s in the positive x-direction
Vy = -1.2m/s in the negative y-direction.