Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

Problem 36a

Chapter 2, Problem 36a

A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$ -m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. What is the speed of the rock just before it hits the street?

Verified step by step guidance

Identify the initial conditions: The initial velocity of the rock is 22.0 m/s upward, and it is thrown from a height of 30.0 m above the street.

Use the kinematic equation for velocity to find the final speed just before the rock hits the street. The equation is:

v = v

₀+gt, where

v

is the final velocity,

v

₀ is the initial velocity,

g

is the acceleration due to gravity (approximately 9.81 m/s²), and

t

is the time of flight.

To find the time of flight, use the kinematic equation for displacement:

y = y

₀+v₀t+12gt^2, where

y

is the final position (0 m, since it lands on the street),

y

₀ is the initial position (30.0 m), and solve for

t

Substitute the value of

t

obtained from the displacement equation into the velocity equation to find the final velocity

v

Remember that the final speed is the magnitude of the final velocity, so take the absolute value of

v

to find the speed just before the rock hits the street.

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Key Concepts

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

Kinematics Equations

Kinematics equations describe the motion of objects without considering the forces that cause the motion. For vertical motion, these equations relate initial velocity, final velocity, acceleration due to gravity, displacement, and time. They are essential for calculating the speed of the rock just before it hits the street.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed. In this scenario, the rock's initial kinetic energy and potential energy are converted into kinetic energy as it falls. This concept helps determine the rock's speed upon impact by equating initial and final energy states.

Gravitational Acceleration

Gravitational acceleration is the acceleration of an object due to Earth's gravity, approximately 9.81 m/s² downward. It affects the rock's motion as it travels upward and downward, influencing its velocity and displacement. Understanding this constant is crucial for applying kinematics equations to solve the problem.

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Related Practice

Textbook Question

You throw a glob of putty straight up toward the ceiling, which is $3.60$ m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is $9.50$ m/s. What is the speed of the putty just before it strikes the ceiling?

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Textbook Question

If a flea can jump straight up to a height of $0.440$ m, what is its initial speed as it leaves the ground?

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Textbook Question

If a flea can jump straight up to a height of $0.440$ m, How long is it in the air?

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Textbook Question

A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$ -m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. How much time elapses from when the rock is thrown until it hits the street?

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Textbook Question

A juggler throws a bowling pin straight up with an initial speed of $8.20$ m/s. How much time elapses until the bowling pin returns to the juggler's hand?

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Textbook Question

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of $2.80$ m/s². At the same instant a truck, traveling with a constant speed of $20.0$ m/s, overtakes and passes the car. How fast is the car traveling when it overtakes the truck?

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A small rock is thrown vertically upward with a speed of 22.022.0 m/s from the edge of the roof of a 30.030.0-m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. What is the speed of the rock just before it hits the street?

Verified video answer for a similar problem:

Key Concepts

Kinematics Equations

Conservation of Energy

Gravitational Acceleration

A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$ -m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. What is the speed of the rock just before it hits the street?