What Is the Minimum Radius for Safe Flight at 100 m/s?

In summary, the pilot of an airplane flying in a horizontal circle at a speed of 100 m/s wants to keep his centripetal acceleration below 7.00 times free-fall acceleration. Using the equations v=eπr/t and a=v^2/t, the pilot calculates a time of 145.6 seconds and a radius of 2318 meters. However, after realizing a mistake in the calculation, the pilot changes the time to radius and gets a correct answer of 145.6 meters.
  • #1
mortho
100
0

Homework Statement


An airplane is flying in a horizontal circle at a speed of 100 m/s. The 88.0 kg pilot does not want his centripetal acceleration to exceed 7.00 times free-fall acceleration.
a) What is the minimum radius of the circular path?

Homework Equations


v=eπr/t

a=v2/t

The Attempt at a Solution



So i figured out the time using the acceleration equation which was 68.67=100squred/t and for t i got 145.6 s. Then i used that time to solve for radius and got 2318 m which was wrong. The only thing i could think of that i did wrong was something mathematical. Help Please!:)
 
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  • #2
Change the t to an r like we talked about in your other thread and you should be OK.
 
  • #3
so ..145.6 m ?
 
  • #4
Looks good to me.
 
  • #5
Thanks!
 

FAQ: What Is the Minimum Radius for Safe Flight at 100 m/s?

What is the minimum radius and why is it important?

The minimum radius is the smallest possible distance from the center of a circle to its circumference. It is important because it determines the size and shape of the circle, and can also impact its stability and strength in certain applications.

How do you calculate the minimum radius of a circle?

To calculate the minimum radius of a circle, you can use the formula r = √(A/π), where r is the radius and A is the area of the circle. Alternatively, you can also use the formula r = c/2π, where c is the circumference of the circle.

What factors can affect the minimum radius of a circle?

The minimum radius of a circle can be affected by various factors, including the size and shape of the circle, the material it is made of, and the forces acting upon it. In some cases, external factors such as temperature and pressure can also impact the minimum radius.

Can the minimum radius of a circle ever be negative?

No, the minimum radius of a circle cannot be negative. It is always a positive value, as the distance from the center of a circle to its circumference cannot be less than zero.

How does finding the minimum radius relate to other mathematical concepts?

Finding the minimum radius of a circle is related to other mathematical concepts such as circumference, diameter, and area. It also involves the use of formulas and equations, making it a fundamental part of geometry and trigonometry.

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