What is the mathematical relationship bewtween pressure and displacement?

[tenbee]

Homework Statement

I'm having trouble understanding the relationship between pressure, speed, and displacement to answer the following question correctly:

While you are stopped at an intersection turn lane, a large truck zooms by, just a few feet from your car. As the truck passes, your car will be:

A) pulled towards the truck, because the increased wind speed between the truck and the car lowers the pressure there.
B) pushed away from the truck, because the increased wind speed between the truck and the car lowers the pressure there.
C) pulled towards the truck, because the increased wind speed between the truck and the car increases the pressure there.
D) pushed away from the truck, because the increased wind speed between the truck and the car increases the pressure there.

Correct Answer: A

Homework Equations

Bernoulli's equation P + ρgy +1/2ρv^2 = K where P is pressure and ρ is density

The Attempt at a Solution

I was able to rule-out C and D from Bernoulli's equation P + ρgy +1/2ρv^2 = K where P is pressure and ρ is density... as velocity or speed increases, P must decrease. Now physically I've seen this exact scenario happen in slow motion (on some luxury car commercial), but mathematically I do not see the relationship between P and displacement.

Using equations without calculus, please demonstrate the relationship between pressure and displacement.

 

[Dick]

"pushed" and "pulled" relate to force, not displacement. If the pressure between you and the truck is less than the pressure on the other side of you, is the force going to be towards the truck or away from the truck? That part of the question is about the relation between pressure and force.

 

[tenbee]

"pushed" and "pulled" relate to force, not displacement. If the pressure between you and the truck is less than the pressure on the other side of you, is the force going to be towards the truck or away from the truck? That part of the question is about the relation between pressure and force.

AHHHHHHH... yes, yes - I forgot about the force on the other side of the car! Thanks so much.