Wind resistance is jointly proportional to velocity and surface area of the object. If an object is traveling 45 mph and has a surface area of 49 square feet it will experience a wind resistance of 496.125 Newtons. How fast must an object be moving to experience a wind resistance of 164.25 Newtons if it has a surface area of 10 square feet

Given:

Velocity, v1 = 45 mph

Converting from mph to m/s,

45 mi/h * 1609.3 m/1 mi * 1 h/3600 s

= 20.12 m/s

surface area, A1 = 49 square feet

Converting ft^2 to m^2,

49 ft^2 * (0.305 m) ^2 / (1 ft) ^2

= 4.56 m^2

Wind resistance, R1 = 496.125 Newtons.

Wind resistance, R2 = 164.25 Newtons

Surface area, A2 = 10 square feet

Converting ft^2 to m^2,

10 ft^2 * (0.305 m) ^2 / (1 ft) ^2

= 0.93 m^2

Wind resistance, R is jointly proportional to velocity, v and surface area of the object, A

R = k (v * A)

R1 / (v1 * A1) = R2 / (v2 * A2)

v2 = R2 * (v1 * A1) / (R1 * A2)

= 164.25 * (20.12 * 4.56) / (496.125 * 0.93)

= 32.66 m/s

Converting from m/s to mph,

32.66 m/s * 1 mi/1609.3 m * 3600 s/1 h

= 73.06 mph

an object will be moving 73 mph to experience a wind resistance of 164.25 Newtons if it has a surface area of 10 square feet

Explanation:

given information:

object speed, v₁ = 45 mph

surface area, s₁ = 49 ft²

wind resistance, R₁ = 496.125 N

if

R₂ = 164.25 N

s₂ = 10 ft²

v₂ = ?

first we need to find the k from the first case. we know that

R₁ = k v₁ s₁

k = R / (v s)

= 496.125 / (45 x 49)

= 0.225

now we can find the v₂

R₂ = k v₂ s₂

v₂ = R₂ / k s₂

= 164.25 / (0.225 x 10)

= 73 mph