To solve this problem, we need to apply the principle of conservation of momentum. This principle states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. Let's break it down step by step.
Understanding the Problem
We have two gliders:
- Glider 1 (mass m1 = 1.25 kg) moving at an initial velocity of 3.62 m/s.
- Glider 2 (mass m2 = 2.30 kg) is initially at rest (velocity = 0 m/s).
After the collision, glider 1 moves with a velocity of 1.07 m/s. We need to find the velocity of glider 2 after the collision, which we'll denote as v2.
Applying Conservation of Momentum
The total momentum before the collision can be calculated as follows:
- Momentum of glider 1 before collision = m1 * initial velocity of glider 1 = 1.25 kg * 3.62 m/s
- Momentum of glider 2 before collision = m2 * initial velocity of glider 2 = 2.30 kg * 0 m/s = 0
Thus, the total momentum before the collision is:
P_initial = (1.25 kg * 3.62 m/s) + 0 = 4.525 kg·m/s
Calculating Momentum After the Collision
After the collision, the momentum of each glider can be expressed as:
- Momentum of glider 1 after collision = m1 * final velocity of glider 1 = 1.25 kg * 1.07 m/s
- Momentum of glider 2 after collision = m2 * final velocity of glider 2 = 2.30 kg * v2
The total momentum after the collision is:
P_final = (1.25 kg * 1.07 m/s) + (2.30 kg * v2)
Setting Up the Equation
According to the conservation of momentum:
P_initial = P_final
Substituting the values we calculated:
4.525 kg·m/s = (1.25 kg * 1.07 m/s) + (2.30 kg * v2)
Calculating the momentum of glider 1 after the collision:
1.25 kg * 1.07 m/s = 1.3375 kg·m/s
Now we can substitute this back into our equation:
4.525 kg·m/s = 1.3375 kg·m/s + (2.30 kg * v2)
Solving for v2
To find v2, we rearrange the equation:
2.30 kg * v2 = 4.525 kg·m/s - 1.3375 kg·m/s
2.30 kg * v2 = 3.1875 kg·m/s
Now, divide both sides by 2.30 kg:
v2 = 3.1875 kg·m/s / 2.30 kg
v2 ≈ 1.39 m/s
Considering Direction
Since glider 2 was initially at rest and the collision occurred in the same direction as glider 1's initial motion, we can conclude that glider 2 is moving forward after the collision. Therefore, the velocity of glider 2 after the collision is approximately:
v2 ≈ 1.39 m/s
Choosing the Correct Answer
Among the options provided, the closest value to our calculated result is:
d. 1.37 m/s
Thus, the velocity of glider 2 after the collision is approximately 1.37 m/s in the same direction as glider 1's initial motion.
