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 is the magnitude of its velocity 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 46c

2장, 문제 46c

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 is the magnitude of its velocity at the highest point?

검증된 단계별 안내

Understand that at the highest point of its trajectory, the egg's velocity is zero because it momentarily stops before reversing direction.

Use the kinematic equation for vertical motion:

v_{f} = v_{i} - g t

, where

v_{f}

is the final velocity,

v_{i}

is the initial velocity,

g

is the acceleration due to gravity (approximately

9.8

m/s²), and

t

is the time.

Since the velocity at the highest point is zero, set

v_{f}

to zero and solve for the initial velocity

v_{i}

using the time it takes to reach the highest point.

Determine the time to reach the highest point by considering that the total time for the upward and downward journey is 5.00 s. The time to reach the highest point is half of this total time.

Substitute the known values into the kinematic equation to find the initial velocity, which will help in understanding the motion of the egg.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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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, with its vertical motion influenced by gravity. Understanding this helps in analyzing the egg's velocity and position at different times.

Velocity at the Highest Point

At the highest point of its trajectory, the vertical component of the projectile's velocity is zero. This is because gravity decelerates the upward motion until the object momentarily stops before descending. Recognizing this concept is crucial for determining the egg's velocity at the peak of its path.

Acceleration Due to Gravity

The acceleration due to gravity is a constant force acting on objects near Earth's surface, typically approximated as 9.81 m/s² downward. It affects the egg's motion by slowing its ascent and accelerating its descent. This concept is essential for calculating the egg's velocity and position at various points in its trajectory.