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wind resistance varies jointly as an objects surface area and velocity. if an object traveling at 55 miles per hour with a surface area of 20 square feet experiences a wind resistance of 220 newtons how fast must a car with 55 square feet of surface area travel in order to experience a wind resistance of 275 newtons?​

Respuesta :

MrRoyal

Answer:

25 miles per hour

Step-by-step explanation:

Given

[tex]W = Wind\ resistance[/tex]

[tex]A = Surface\ Area[/tex]

[tex]V = Velocity[/tex]

The joint variation can be represented as:

[tex]W\ \alpha\ A*V[/tex]

Where:

[tex]V = 55; A = 20; W = 220[/tex]

Required

Find V,  when: [tex]A = 55; W = 275[/tex]

We have:

[tex]W\ \alpha\ A*V[/tex]

Express as an equation

[tex]W= k *A*V[/tex]

Where k is the constant of variation

Make k the subject

[tex]k = \frac{W}{A*V}[/tex]

When: [tex]V = 55; A = 20; W = 220[/tex]

We have:

[tex]k = \frac{220}{20 *55 }[/tex]

[tex]k = \frac{220}{1100}[/tex]

[tex]k = 0.2[/tex]

When: [tex]A = 55; W = 275[/tex]

We have:

[tex]k = \frac{W}{A*V}[/tex]

Substitute: [tex]A = 55; W = 275[/tex] and [tex]k = 0.2[/tex]

[tex]0.2 = \frac{275}{55 * V}[/tex]

Make V the subject

[tex]V= \frac{275}{55 * 0.2}[/tex]

[tex]V= \frac{275}{11}[/tex]

[tex]V= 25[/tex]

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