A 3.0-kg mass moving in the positive x direction with a speed of 10 m/s collides with a 6.0-kg mass initially at rest. After the collision, the speed of the 3.0-kg mass is 8.0 m/s, and its velocity vector makes an angle of 35° with the positive x axis. What is the magnitude of the velocity of the 6.0-kg mass after the collision?
A) 2.2 m/s
B) 2.9 m/s
C) 4.2 m/s
D) 3.5 m/s
E) 4.7 m/s

Question

Quizplus · Accepted Answer

To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision. Before the collision, the total momentum is given by the momentum of the 3.0-kg mass, since the 6.0-kg mass is at rest. After the collision, we have to consider the momentum of both masses.Before collision:- Momentum of 3.0-kg mass = $3.0 \, \text{kg} \times 10 \, \text{m/s} = 30 \, \text{kg} \cdot \text{m/s}$.- Momentum of 6.0-kg mass = $6.0 \, \text{kg} \times 0 \, \text{m/s} = 0 \, \text{kg} \cdot \text{m/s}$.- Total momentum before collision = $30 \, \text{kg} \cdot \text{m/s}$.After collision:- Momentum of 3.0-kg mass in the x-direction = $3.0 \, \text{kg} \times 8.0 \, \text{m/s} \times \cos(35^\circ)$.- To find the velocity of the 6.0-kg mass, we need to ensure the total momentum in the x-direction is conserved.Let $v$ be the velocity of the 6.0-kg mass after the collision. The total momentum in the x-direction after the collision is the sum of the x-components of the momenta of the two masses. Setting this equal to the total momentum before the collision and solving for $v$ gives us the magnitude of the velocity of the 6.0-kg mass. Using the conservation of momentum and solving for $v$, we find that the correct answer is 2.9 m/s, which corresponds to choice B. This calculation involves breaking down the momentum of the 3.0-kg mass into its x and y components, using the given angle, and ensuring the total x-component of the momentum is conserved before and after the collision.

A 30-Kg Mass Moving in the Positive X Direction with a a Speed