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Ch 02: Kinematics in One Dimension
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Knight Calc 5th EditionCh 02: Kinematics in One Dimension문제 80
2장, 문제 80

A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0 s later. What was the rocket's acceleration?

검증된 단계별 안내
1
Define the motion of the rocket and the bolt. The rocket is moving upward with constant acceleration, and the bolt detaches after 4 seconds. The bolt then follows a free-fall motion under gravity after detachment. Use kinematic equations to analyze both motions.
Determine the velocity of the rocket (and the bolt) at the moment the bolt detaches. Use the kinematic equation: v=u+at, where u is the initial velocity (0 m/s), a is the rocket's acceleration, and t is 4 seconds.
Calculate the height of the bolt at the moment it detaches from the rocket. Use the kinematic equation: s=ut+12at^2, where s is the height, u is 0 m/s, a is the rocket's acceleration, and t is 4 seconds.
Analyze the motion of the bolt after detachment. The bolt starts with an initial upward velocity equal to the rocket's velocity at detachment and is subject to gravitational acceleration (g=9.8 m/s^2). Use the kinematic equation: s=vt+12at^2 to find the total displacement of the bolt during its free fall.
Combine the equations for the rocket's motion and the bolt's motion to solve for the rocket's acceleration. Use the fact that the total time for the bolt to hit the ground after detachment is 6 seconds, and the displacement of the bolt relative to the ground is zero when it lands.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

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

Constant Acceleration

Constant acceleration refers to a situation where an object's velocity changes at a steady rate over time. In the context of the rocket, this means that the rocket's speed increases uniformly as it ascends. This concept is crucial for determining the rocket's motion and the time it takes for the bolt to fall after detaching.
추천 영상:
가이드 코스
08:59
Phase Constant of a Wave Function

Free Fall

Free fall describes the motion of an object under the influence of gravity alone, with no other forces acting on it. Once the bolt detaches from the rocket, it enters free fall, accelerating downward at approximately 9.81 m/s². Understanding free fall is essential for calculating the time it takes for the bolt to hit the ground after it falls off the rocket.
추천 영상:
가이드 코스
08:36
Vertical Motion & Free Fall

Kinematic Equations

Kinematic equations are mathematical formulas that describe the motion of objects under constant acceleration. These equations relate displacement, initial velocity, final velocity, acceleration, and time. They are vital for solving problems involving the rocket's ascent and the bolt's descent, allowing us to find the rocket's acceleration based on the given time intervals.
추천 영상:
가이드 코스
08:25
Kinematics Equations
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