Ch. 02 - Describing Motion: Kinematics in One Dimension

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 02 - Describing Motion: Kinematics in One Dimension

문제 64c

2장, 문제 64c

A rocket rises vertically, from rest, with an acceleration of 3.2 m/s² until it runs out of fuel at an altitude of 725 m. After this point, its acceleration is that of gravity, downward. What maximum altitude does the rocket reach?

검증된 단계별 안내

Determine the velocity of the rocket at the moment it runs out of fuel. Use the kinematic equation:

v^2 = v_0^2 + 2a d

, where

v_0 = 0

(initial velocity),

a = 3.2 \(\text{ m/s}\)^2

(acceleration), and

d = 725 \(\text{ m}\)

(distance traveled while fuel is burning). Solve for

v

Once the rocket runs out of fuel, it continues to move upward due to its velocity at that point. Its motion is now under the influence of gravity alone, with an acceleration of

a = -9.8 \(\text{ m/s}\)^2

. Use the kinematic equation

v^2 = v_0^2 + 2a d

again, where

v = 0

(velocity at the maximum altitude),

v_0

is the velocity calculated in step 1, and

a = -9.8 \(\text{ m/s}\)^2

. Solve for

d

, which represents the additional height the rocket travels after running out of fuel.

Add the altitude at which the rocket runs out of fuel (

725 \(\text{ m}\)

) to the additional height calculated in step 2 to find the maximum altitude reached by the rocket.

Verify the units and ensure all calculations are consistent with the SI system. Double-check the signs of acceleration and velocity to ensure they align with the direction of motion.

Summarize the process: The maximum altitude is the sum of the altitude at fuel exhaustion and the additional height gained while decelerating under gravity. This ensures a clear understanding of the problem-solving approach.

비슷한 문제에 대한 검증된 영상 답변:

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.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This principle is crucial for understanding how the rocket accelerates upward due to the thrust generated by its engines until it runs out of fuel.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. In this scenario, we can use these equations to calculate the rocket's velocity at the moment it runs out of fuel and subsequently determine its maximum altitude by considering the motion under the influence of gravity alone.

Free Fall and Gravity

Once the rocket runs out of fuel, it enters free fall, where the only force acting on it is gravity, which accelerates it downward at approximately 9.81 m/s². Understanding free fall is essential for calculating how high the rocket ascends after it exhausts its fuel and begins to decelerate until it reaches its peak altitude.