Ch 03: Motion in Two or Three Dimensions

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo

Young & Freedman Calc 14th Edition

Ch 03: Motion in Two or Three Dimensions

Problema 22c

Capitolo 3, Problema 22c

A 124 kg balloon carrying a 22 kg basket is descending with a constant downward velocity of 20.0 m/s. A 1.0 kg stone is thrown from the basket with an initial velocity of 15.0 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 5.00 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 20.0 m/s. At the instant the rock hits the ground, how far is it from the basket?

Guida verificata passo dopo passo

First, determine the vertical distance the stone travels. Since the stone is thrown perpendicular to the balloon's descent, its initial vertical velocity is the same as the balloon's, which is 20.0 m/s downward. Use the formula for distance:

d = v t

, where

v

is the velocity and

t

is the time.

Calculate the vertical distance the stone falls in 5.00 seconds using the formula:

d = v t

. Substitute

v

with 20.0 m/s and

t

with 5.00 s.

Next, determine the horizontal distance traveled by the stone. The stone is thrown with an initial horizontal velocity of 15.0 m/s. Use the formula for horizontal distance:

d = v t

, where

v

is the horizontal velocity and

t

is the time.

Calculate the horizontal distance the stone travels in 5.00 seconds using the formula:

d = v t

. Substitute

v

with 15.0 m/s and

t

with 5.00 s.

Finally, use the Pythagorean theorem to find the total distance from the basket to the stone when it hits the ground. The vertical and horizontal distances form a right triangle, so the total distance is given by:

d = \sqrt{d^{2} + d^{2}}

, where

d

represents the vertical and horizontal distances.

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Relative Velocity

Relative velocity is the velocity of an object as observed from a particular frame of reference. In this problem, the stone's velocity is given relative to the basket, which is itself moving. Understanding how to convert this relative velocity to an absolute velocity with respect to the ground is crucial for solving the problem.

Video consigliato:

Percorso guidato

04:27

Intro to Relative Motion (Relative Velocity)

Projectile Motion

Projectile motion describes the motion of an object thrown into the air, subject to only the acceleration of gravity. The stone, once thrown, follows a projectile path. Analyzing its horizontal and vertical components separately allows us to determine its trajectory and final position when it hits the ground.

Video consigliato:

Percorso guidato

04:44

Introduction to Projectile Motion

Vector Addition

Vector addition is the process of combining vectors to determine a resultant vector. In this scenario, the stone's velocity relative to the basket and the basket's velocity relative to the ground must be added vectorially to find the stone's velocity relative to the ground, which is essential for calculating the stone's displacement.

Video consigliato:

Percorso guidato

07:30

Vector Addition By Components

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