Ch 02: Kinematics in One Dimension

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 02: Kinematics in One Dimension

Problema 23

Capitolo 2, Problema 23

As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 35 m/s. How fast is the watermelon going when it passes Superman?

Guida verificata passo dopo passo

Identify the key variables: The initial height of the watermelon is 320 m, its initial velocity is 0 m/s (since it is dropped), and Superman's initial velocity is 35 m/s downward. The acceleration due to gravity is approximately 9.8 m/s².

Write the equation for the position of the watermelon as a function of time:

y = y i_{0} + v_{i} t + \frac{1}{2} g t ²

, where

v_{i}

is the initial velocity (0 m/s for the watermelon),

g

is the acceleration due to gravity, and

t

is time.

Write the equation for the position of Superman as a function of time:

y = y i_{0} + v_{i} t

, where

v_{i}

is Superman's initial velocity (35 m/s downward).

Set the two position equations equal to each other to find the time

t

when the watermelon passes Superman. Solve for

t

by equating the two equations and simplifying.

Once the time

t

is found, use the velocity equation for the watermelon:

v = v_{i} + g t

. Substitute the value of

t

to calculate the velocity of the watermelon when it passes Superman.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

12m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Free Fall

Free fall refers to the motion of an object under the influence of gravity alone, with no air resistance. In this scenario, the watermelon is in free fall after being dropped, meaning it accelerates downward at approximately 9.81 m/s², the acceleration due to gravity. This concept is crucial for determining the watermelon’s velocity at any point during its descent.

Video consigliato:

Percorso guidato

08:36

Vertical Motion & Free Fall

Relative Velocity

Relative velocity is the velocity of one object as observed from another object. In this case, we need to consider the speed of Superman as he descends at 35 m/s and compare it to the speed of the watermelon. Understanding relative velocity helps us determine how fast the watermelon is moving when it passes Superman, as we must account for both their speeds.

Video consigliato:

Percorso guidato

04:27

Intro to Relative Motion (Relative Velocity)

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They can be used to calculate the final velocity of the watermelon just before it passes Superman. By applying the appropriate kinematic equation, we can find the watermelon’s speed after falling a certain distance, which is essential for solving the problem.

Video consigliato:

Percorso guidato

08:25

Kinematics Equations

Pratica correlata

Domanda del libro di testo

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall. What is the bearing's impact velocity?

1641

views

Domanda del libro di testo

A skier is gliding along at 3.0 m/s on horizontal, frictionless snow. He suddenly starts down a 10° incline. His speed at the bottom is 15 m/s. What is the length of the incline?

2264

views

rank

Domanda del libro di testo

When jumping, a flea accelerates at an astounding 1000 m/s², but over only the very short distance of 0.50 mm. If a flea jumps straight up, and if air resistance is neglected (a rather poor approximation in this situation), how high does the flea go?

Domanda del libro di testo

A rock is tossed straight up from ground level with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep. What is the rock's speed as it hits the bottom of the hole?

3948

views

Domanda del libro di testo

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?

2873

views

Domanda del libro di testo

A car traveling at 30 m/s runs out of gas while traveling up a 10° slope. How far up the hill will it coast before starting to roll back down?

3690

views