I'm working on functions in algebra two and now they've added word problems. How can p=s=0? And how do I solve this question?

Question

"The dynamic pressure (P) on the wall increased with the square of the speed (s) Initially, P=s=0. At a speed of 30, the pressure was 15. What is a function that represents pressure as a function of airspeed?"

Answer 1

The statement p = s = 0 just means that when the airspeed is zero, the dynamic pressure is also zero. You can solve this problem using a proportionality relation. You were given that dynamic pressure is proportional to the square of the airspeed, so the function has the form

P(s) = ks²

where k is a constant. Now use the given data to solve for k and complete the function.

15 = k 30² ⇒

k = 15/30² = 0.0167 (with roundoff)

The function is

P(s) = 0.0167s²