Jack (mass 55.0 kg) is sliding due east with speed 8.00 m/s on the surface of a frozen pond. He collides with Jill (mass 48.0 kg), who is initially at rest. After the collision, Jack is traveling at 5.00 m/s in a direction 34.0° north of east. What is Jill's velocity (magnitude and direction) after the collision? Ignore friction.

검증된 단계별 안내

Step 1: Identify the type of collision. Since the problem involves two objects colliding and no external forces are acting (ignoring friction), this is a conservation of momentum problem. Momentum is conserved in both the x-direction (east-west) and the y-direction (north-south).

Step 2: Write the equation for conservation of momentum in the x-direction. The total momentum before the collision in the x-direction is the momentum of Jack (mass × velocity) since Jill is initially at rest. After the collision, the x-component of Jack's momentum and Jill's momentum must sum to the initial momentum. Use the equation: \( m_{Jack} v_{Jack, initial} = m_{Jack} v_{Jack, final} \cos(\theta) + m_{Jill} v_{Jill} \cos(\phi) \), where \( \theta \) is Jack's angle (34.0° north of east) and \( \phi \) is Jill's unknown direction.

Step 3: Write the equation for conservation of momentum in the y-direction. Since there is no initial momentum in the y-direction (north-south), the total momentum in the y-direction after the collision must be zero. Use the equation: \( m_{Jack} v_{Jack, final} \sin(\theta) = m_{Jill} v_{Jill} \sin(\phi) \).

Step 4: Solve the system of equations. You now have two equations: one for the x-direction and one for the y-direction. Solve these equations simultaneously to find Jill's velocity \( v_{Jill} \) and direction \( \phi \). Use trigonometric relationships to isolate \( v_{Jill} \) and \( \phi \).

Step 5: Interpret the results. Once you solve for \( v_{Jill} \) (magnitude of Jill's velocity) and \( \phi \) (direction of Jill's velocity), ensure the direction is expressed relative to east (e.g., degrees north or south of east). This will give you the final answer in terms of magnitude and direction.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

16m

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Conservation of Momentum

The principle of conservation of momentum states that in a closed system, the total momentum before an event (like a collision) is equal to the total momentum after the event. This is crucial for solving collision problems, as it allows us to set up equations based on the initial and final velocities and masses of the objects involved.

Vector Components

In physics, vectors can be broken down into their components along the axes of a coordinate system. For this problem, we can resolve the velocities into east-west (x-axis) and north-south (y-axis) components. This simplification is essential for accurately calculating the resultant velocity of Jill after the collision.

Collision Types

Collisions can be classified as elastic or inelastic, with inelastic collisions conserving momentum but not kinetic energy. In this scenario, since Jack and Jill collide and move together afterward, we assume an inelastic collision, which affects how we calculate the final velocities and directions of the objects involved.