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 24b

Chapter 2, Problem 24b

A pilot who accelerates at more than $4 g$ begins to 'gray out' but doesn't completely lose consciousness. How far would the plane travel during this period of acceleration? (Use $331$ m/s for the speed of sound in cold air.)

Verified step by step guidance

First, understand that '4g' refers to an acceleration that is four times the acceleration due to gravity, where g is approximately 9.81 m/s². Therefore, the acceleration of the plane is 4 × 9.81 m/s².

Next, identify the initial velocity of the plane. Since the problem mentions the speed of sound in cold air as 331 m/s, we can assume this is the initial velocity of the plane.

To find the distance traveled during the acceleration, use the kinematic equation:

d = v

₀t+12at^2, where d is the distance, v₀ is the initial velocity, a is the acceleration, and t is the time.

Determine the time period of acceleration. This might require additional information or assumptions, such as the duration for which the pilot can withstand 4g acceleration without losing consciousness.

Finally, substitute the known values (initial velocity, acceleration, and time) into the kinematic equation to solve for the distance traveled during the acceleration period.

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Key Concepts

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

Acceleration

Acceleration is the rate of change of velocity of an object. It is a vector quantity, meaning it has both magnitude and direction. In this context, the pilot experiences an acceleration of more than 4g, where g is the acceleration due to gravity (approximately 9.81 m/s²). Understanding acceleration is crucial for calculating the distance traveled during this period.

Distance Traveled Under Constant Acceleration

The distance traveled by an object under constant acceleration can be calculated using the kinematic equation: d = v_i * t + 0.5 * a * t², where d is the distance, v_i is the initial velocity, a is the acceleration, and t is the time. This formula helps determine how far the plane travels while accelerating at more than 4g.

Speed of Sound

The speed of sound is the speed at which sound waves travel through a medium, such as air. In this problem, the speed of sound is given as 331 m/s in cold air, which may be used to compare the plane's velocity during acceleration. Understanding the speed of sound is important for contextualizing the plane's speed relative to sound waves.

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Related Practice

Textbook Question

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of $20$ m/s ( $45$ mi/h) when it reaches the end of the $120$ -m-long ramp. How much time does it take the car to travel the length of the ramp?

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Textbook Question

A pilot who accelerates at more than $4 g$ begins to 'gray out' but doesn't completely lose consciousness. Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach $4$ (four times the speed of sound) without graying out? (Use $331$ m/s for the speed of sound in cold air.)

In the fastest measured tennis serve, the ball left the racquet at $73.14$ m/s. A served tennis ball is typically in contact with the racquet for $30.0$ ms and starts from rest. Assume constant acceleration. What was the ball's acceleration during this serve?

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Textbook Question

The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than $250$ m/s². If you are in an automobile accident with an initial speed of $105$ km/h ( $65$ mi/h) and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

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Textbook Question

At launch a rocket ship weighs $4.5$ million pounds. When it is launched from rest, it takes $8.00$ s to reach $161$ km/h; at the end of the first $1.00$ min, its speed is $1610$ km/h. What is the average acceleration (in m/s²) of the rocket (i) during the first $8.00$ s and (ii) between $8.00$ s and the end of the first $1.00$ min?

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A pilot who accelerates at more than 4g4g begins to 'gray out' but doesn't completely lose consciousness. How far would the plane travel during this period of acceleration? (Use 331331 m/s for the speed of sound in cold air.)

Verified video answer for a similar problem:

Key Concepts

Acceleration

Distance Traveled Under Constant Acceleration

Speed of Sound

A pilot who accelerates at more than $4 g$ begins to 'gray out' but doesn't completely lose consciousness. How far would the plane travel during this period of acceleration? (Use $331$ m/s for the speed of sound in cold air.)