Question

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?​

Answer 1

Answer:

25 miles per hour

Step-by-step explanation:

Given

$W = Wind\ resistance$

$A = Surface\ Area$

$V = Velocity$

The joint variation can be represented as:

$W\ \alpha\ A*V$

Where:

$V = 55; A = 20; W = 220$

Required

Find V,  when: $A = 55; W = 275$

We have:

$W\ \alpha\ A*V$

Express as an equation

$W= k *A*V$

Where k is the constant of variation

Make k the subject

$k = \frac{W}{A*V}$

When: $V = 55; A = 20; W = 220$

We have:

$k = \frac{220}{20 *55 }$

$k = \frac{220}{1100}$

$k = 0.2$

When: $A = 55; W = 275$

We have:

$k = \frac{W}{A*V}$

Substitute: $A = 55; W = 275$ and $k = 0.2$

$0.2 = \frac{275}{55 * V}$

Make V the subject

$V= \frac{275}{55 * 0.2}$

$V= \frac{275}{11}$

$V= 25$