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 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

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Young & Freedman Calc 15th Edition

Ch 02: Motion Along a Straight Line

Problem 44d

Chapter 2, Problem 44d

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?

Verified step by step guidance

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Textbook Question

A large boulder is ejected vertically upward from a volcano with an initial speed of $40.0$ m/s. Ignore air resistance. At what time after being ejected is the boulder moving at $20.0$ m/s upward?

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Textbook Question

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 initial speed of the egg?

A large boulder is ejected vertically upward from a volcano with an initial speed of $40.0$ m/s. Ignore air resistance. At what time is it moving at $20.0$ m/s downward?

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Textbook Question

A $15$ -kg rock is dropped from rest on the earth and reaches the ground in $1.75$ s. When it is dropped from the same height on Saturn's satellite Enceladus, the rock reaches the ground in $18.6$ s. What is the acceleration due to gravity on Enceladus?

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