An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point 30.030.030.0 m below its starting point 5.005.005.00 s after it leaves the thrower's hand. Ignore air resistance. What are the magnitude and direction of its acceleration at the highest point?

Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

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Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

문제 46d

2장, 문제 46d

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point $30.0$ m below its starting point $5.00$ s after it leaves the thrower's hand. Ignore air resistance. What are the magnitude and direction of its acceleration at the highest point?

검증된 단계별 안내

Recognize that the problem involves projectile motion, specifically vertical motion under gravity. The key point here is to understand that the only force acting on the egg is gravity, which affects its acceleration.

Recall that the acceleration due to gravity is constant and acts downward. This is a fundamental concept in physics, where the acceleration due to gravity is approximately 9.81 m/s² near the surface of the Earth.

At the highest point of its trajectory, the egg's velocity is zero because it momentarily stops before starting to fall back down. However, the acceleration due to gravity is still acting on it.

Since the problem asks for the magnitude and direction of the acceleration at the highest point, note that the acceleration remains constant at 9.81 m/s² downward throughout the motion, including at the highest point.

Conclude that the magnitude of the acceleration is 9.81 m/s², and the direction is downward, which is consistent with the acceleration due to gravity acting on the egg at all times during its flight.

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.

Projectile Motion

Projectile motion refers to the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. In this scenario, the egg follows a parabolic trajectory, moving upward and then downward. Understanding the components of its motion, such as initial velocity, maximum height, and time of flight, is crucial for analyzing its behavior.

Acceleration Due to Gravity

The acceleration due to gravity is a constant force that acts on objects in free fall near the Earth's surface, typically denoted as 9.81 m/s² downward. This constant acceleration affects the egg throughout its motion, including at the highest point, where its velocity is momentarily zero but acceleration remains directed downward.

Kinematics at the Highest Point

At the highest point of its trajectory, the egg's vertical velocity is zero, but it still experiences acceleration due to gravity. This means that while the egg momentarily stops moving upward, it immediately begins to accelerate downward. Understanding this helps in determining that the magnitude of acceleration is 9.81 m/s² downward, even at the peak.