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 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 44c

Chapter 2, Problem 44c

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?

Verified step by step guidance

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.

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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, 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.

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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?

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