Direct, Inverse and Joint Variation

Question

The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind blowing at 50 mph exerts a force of 75 pounds on a surface of 500² ft , how much force will a wind of 75 mph place on a surface of 10ft² ?

Answer 1

The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind blowing at 50 mph exerts a force of 75 pounds on a surface of 500² ft , how much force will a wind of 75 mph place on a surface of 10ft² ?

Goal is to Find F₂ which is new force

Step 1: Write the concept/ relationship of joint (direct) variation

F=KAv²

Note that the Force is measured in lbs in this problem.

So

F=75 lbs

Area of surface (A)=500 ft²

Velocity (v)=50 mph

Note they are asking for the square of the velocity

Step 2: Simplify

75=k*500*50²

75=k*500*2500

k=75/(2500*500)

k=75/1,250,000=0.00006

Step 3: Use new k into the constant value where and evaluate

if v₂₌75

F₂=KAv₂²

= (.00006)(500)(75)²=3.375 lbs

Answer for force 2 at 2nd velocity squared is 3.375 lbs