To solve this problem, we can apply 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: momentum = mass × velocity.
Let's denote the mass of the 132-gram object as m1 = 132 grams, the initial velocity of m1 as v1 = 10 m/s, and the mass of the 1188-gram object as m2 = 1188 grams. The initial velocity of m2 is 0 m/s since it is at rest.
Before the collision: Total momentum = m1 × v1 + m2 × v2 (where v2 is the initial velocity of m2, which is 0 m/s)
After the collision, the two masses stick together and move as one object. Let's denote the final velocity of the combined 1320-gram mass as vf.
After the collision: Total momentum = (m1 + m2) × vf
According to the conservation of momentum principle, the total momentum before the collision is equal to the total momentum after the collision:
m1 × v1 + m2 × v2 = (m1 + m2) × vf
Substituting the given values:
132 grams × 10 m/s + 1188 grams × 0 m/s = (132 grams + 1188 grams) × vf
1320 kg·m/s = 1320 grams × vf
Now, we can solve for vf:
vf = 1320 kg·m/s / 1320 grams vf = 1 m/s
Therefore, the final velocity of the combined 1320 grams is 1 m/s.