Question

The power P of a jet of water is jointly proportional to the cross sectional area A and to the cube ofthe velocity V. (a) Write the formula for P. Use lower case k as the proportionality constant. (b) If the velocity is tripled and the cross sectional area is doubled, by what factor will the power increase? Enter a number. Submit Answer Save Progress

Answer 1

a)
`P=kAV^3`

b) 54

Explanation:

a)

If one quantity, A, is jointly proportional to other 2 quantities (B & C), we can write proportionality equation as:

`A=k*B*C`

Where

k is the proportionality constant

Now, for this problem, P is jointly proportional to A and CUBE OF V, so we can write:

`P=kAV^3`

b)

Now velocity, V, is triples, which means it becomes 3V

Also, cross sectional area, A, is doubled, which means it becomes 2A

Let's put these into formula and see the difference:

`P=kAV^3\\P=k(2A)(3V)^3\\P=k(2A)(27V^3)\\P=(2*27)kAV^3\\P=54kAV^3`

So, power is multiplied by a factor of 54. Power becomes 54 times if Area is doubled and velocity is tripled ( as seen ).