A large boulder is ejected vertically upward from a volcano with an initial speed of 40.040.040.0 m/s. Ignore air resistance. At what time is it moving at 20.020.0 m/s downward?

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

모든 교과서

Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

문제 48b

2장, 문제 48b

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?

검증된 단계별 안내

Identify the initial conditions: The boulder is ejected with an initial speed of 40.0 m/s upward. We need to find the time when its speed is 20.0 m/s downward.

Understand the motion: The boulder is subject to gravitational acceleration, which is approximately 9.8 m/s² downward. This will slow it down as it moves upward, stop it momentarily, and then accelerate it downward.

Use the kinematic equation for velocity: The velocity of an object under constant acceleration can be described by the equation:

v = v

_i-gt, where

v

is the final velocity,

v

_i is the initial velocity,

g

is the acceleration due to gravity, and

t

is the time.

Set up the equation: Substitute the known values into the equation. The final velocity

v

is -20.0 m/s (downward),

v

_i is 40.0 m/s, and

g

is 9.8 m/s². The equation becomes:

- 20.0 = 40.0 - 9.8 t

Solve for time

t

: Rearrange the equation to solve for

t

. This involves isolating

t

on one side of the equation:

t = \frac{(40.0 - - 20.0)}{9.8}

. Calculate the value of

t

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Kinematics Equations

Kinematics equations describe the motion of objects under constant acceleration. They are essential for calculating the position, velocity, and time of an object in motion. In this problem, the equations help determine the time at which the boulder reaches a specific velocity while moving downward.

Gravitational Acceleration

Gravitational acceleration is the constant acceleration experienced by objects due to Earth's gravity, approximately 9.81 m/s² downward. This concept is crucial for understanding the motion of the boulder as it moves upward and then downward, affecting its velocity and time of travel.

Velocity Direction

Velocity direction indicates whether an object is moving upward or downward. In this problem, understanding that the boulder initially moves upward and then downward is key to determining when its velocity is 20.0 m/s downward, requiring consideration of both magnitude and direction.