Answer:
Step-by-step explanation:
To determine the velocity of cart B after the elastic collision with cart A, we can use the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity.
Given:
Mass of cart A (m_A) = 40 kg
Initial velocity of cart A (v_Ai) = 12 m/s
Final velocity of cart A (v_Af) = -1.9 m/s (since it moves to the left)
Mass of cart B (m_B) = 55 kg
Initial velocity of cart B (v_Bi) = 0 m/s (since it is initially stationary)
Final velocity of cart B (v_Bf) = ?
Using the principle of conservation of momentum, we can write:
Total momentum before collision = Total momentum after collision
(m_A * v_Ai) + (m_B * v_Bi) = (m_A * v_Af) + (m_B * v_Bf)
(40 kg * 12 m/s) + (55 kg * 0 m/s) = (40 kg * -1.9 m/s) + (55 kg * v_Bf)
480 kgm/s = -76 kgm/s + (55 kg * v_Bf)
To isolate v_Bf, we can rearrange the equation:
(55 kg * v_Bf) = 480 kgm/s - (-76 kgm/s)
(55 kg * v_Bf) = 480 kgm/s + 76 kgm/s
(55 kg * v_Bf) = 556 kg*m/s
Now, we can solve for v_Bf by dividing both sides of the equation by 55 kg:
v_Bf = (556 kg*m/s) / 55 kg
v_Bf ≈ 10.11 m/s
Therefore, the velocity of cart B after the elastic collision is approximately 10.11 m/s.