Question

the drag Force F on a boat varies jointly with the wet surface area a of the boat and the square of the speed s of the boat. a boat with a wet surface area of 50 ft^2 traveling at 7 miles per hour experiences a drag force of 98 N. find the wet surface area of a boat traveling 7.5 miles per hour and experiencing a drag force of 135 N.__ft^2

Answer 1

Let F be the drag force, A the area and s the speed. We are told that F varies jointly with respect to s and A. This means that we have an equation of the form

`F=k\cdot A\cdot s`

where k is a constant. We are told that when A=50 and s=7, then F=98. So we have the equation

`98=k\cdot50\cdot7=k\cdot350`

If we divide both sides by 350, we get

`k=(98)/(350)=(49\cdot2)/(175\cdot2)=(49)/(175)=(7\cdot7)/(25\cdot7)=(7)/(25)`

So our equation becomes

`F=(7)/(25)\cdot A\cdot s`

Now, we want to calculate A, when s=7.5 and F=135. so we have the equation

`135=(7)/(25)\cdot A\cdot7.5`

Note that 7.5=15/2. So we have

`135=(7)/(25)\cdot A\cdot(15)/(2)=(7\cdot5\cdot3)/(5\cdot5\cdot2)\cdot A=(7\cdot3)/(5\cdot2)\cdot A=(21)/(10)\cdot A`

Now, we multiply both sides by 10, so we get

`21A=135\cdot10=1350`

Finally, by dividng both sides by 21, we get

`A=(1350)/(21)=64.2857`

so the wet surface area is approximately 64.29 ft^2