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Blackout? A jet fighter pilot wishes to accelerate from rest at 5$g$ to reach Mach 3 (three times the speed of sound) as quickly as possible. Experimental tests reveal that he will black out if this acceleration lasts for more than 5.0 s. Use 331 $\mathrm{m} / \mathrm{s}$ for the speed of sound. (a) Will the period of acceleration last long enough to cause him to black out? (b) What is the greatest speed he can reach with an acceleration of 5$g$ before blacking out?

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he blacks out245 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 2

Motion along a Straight Line

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rutgers, The State University of New Jersey

University of Washington

Hope College

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

03:33

A jet fighter pilot wishes…

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$\cdot$ If a pilot acceler…

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A pilot who accelerates at…

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If a pilot accelerates at …

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04:33

A supersonic jet traveling…

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$\bullet$ Pilot blackout i…

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Supersonic Jet A supersoni…

So we know the fighter pilot can only accelerate at five g. However, if if he accelerates at five g for longer than five seconds, the pilot will pass out and we need to make of the final equaling three Mach so three times the speed of sound of 331 meters per second. So this will equal 900 and 93 meters per second. Uh, in order to find the time we can save the X Final equals V X initial plus 80. We know that VX initial equal zero. So we can say that the time taken would be the X final divided by the acceleration. So this would simply be 993. Uh, excuse me. Divided by five times 9.8 and this would give us 20.3 seconds. Now 20.3 seconds is much larger than five seconds. Therefore, the pilot, the pilot will most definitely pass out. Um, the this part B, this is a people. This would be for party for part B. However, they're asking us for the maximum speed that he can reach without passing out at that same acceleration. Sweet instead of e x final equals V X Initial plus 80. We know that the ex initial is again zero and this will equal five g So five times 9.8 meters per second and then he can on Lee. Stay at this acceleration. However, for five seconds so T would equal five seconds and we're getting that the maximum velocity at this acceleration would be 245 meters per second. So in order to reach Mach three and speeds that are much higher than 245 meters per second, he's gonna have to accelerate much slowly, much more slowly than at five times the acceleration due to gravity. This will simply be too much pressure on your body and you'll pass out due to the amount of force on your body. That is the end of the solution. Thank you for watching

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