Question

The iting force. F.exerted on an airplane wing varies jointly as the area of the wing's surface and the square of the plane's velocity. The litt ofa wing with an areaof 280 square feet is 31.900 pounds when the plane is going 250 miles per hour. Find the iting force on the wing the plane slow down to 110 miles per hour.Leave the variation constant infraction form or round to at least 5 decimal places. Round off your final answer to the nearest pound)

Answer 1

Step-by-step explanation

In the question, we are told that the lifting force varies jointly as the area of the wings surface and the square of the plane's velocity.

This can be expressed below;

`L\propto AV^2`

Therefore, if we introduce the constant of variation "K" the expression would then give;

`L=KAV^2`

When L= 31,900 pounds and A= 280 square feet and V=250 miles per hour, we will derive the constant of variation below.

`\begin{gathered} 31900=K*250^2*280 \\ K=(31900)/(250^2*280)=(319)/(175000) \end{gathered}`

Since the same area of the plane is being considered, therefore the the lifting force when the plane slows down to 110 miles per hour is give as

`\begin{gathered} L=(319)/(175000)*280*110^2 \\ L=14036\text{ Pounds} \\ L=6175.84 \end{gathered}`

Answer: 6176 pounds