Underwater thrust formula?

[IustitiaPrime]

I'm trying to determine the force needed for one object to displace another object underwater. Specifically, Object A strikes Object B hard enough to jettison it from the seafloor up to sea level/land, let's say the Pacific coastline. I have a timeframe in mind, density & mass of the two objects, and distance traveled, yet don't know how to apply these factors under the liquid medium of the sea and the pressures involved. I'm not asking for easy answers so much as perhaps an equation to simplify things a bit to calculate either the force required to achieve such a feat or the energy output such a collision would yield.

 

[anorlunda]

I'm having trouble visualizing what you are asking about. It is like underwater billiards?

 

[jrmichler]

If we assume that Object A strikes Object B hard enough to push it free from the seafloor with a velocity:

1) Note that velocity and speed are not the same: https://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-and-Velocity.

2) After Object B is free from the seafloor with a velocity, it is subject to forces:

2a) A buoyancy force. Search buoyancy force for more information.
2b) A drag force. Search drag force and drag coefficient for more information.
2c) Depending on the shape of Object B, there may be a lift force. Search lift coefficient for more information.
2d) Ocean currents. The lift and drag forces are functions of the object velocity relative to the local water velocity and the object shape.
2e) Acceleration force.

Since these forces sum to zero, the remaining unknown is the acceleration. Then you integrate all of the above until the object gets to wherever it gets. It's an easy numerical integration, but difficult to impossible to do it analytically. You get your answer by writing a program to solve the problem for a given Object B velocity, then iterate that velocity (both speed and direction) until you are satisfied with the answer. Then calculate the Object A velocity needed to get the Object B velocity that you found.

A collision has energy output if it sets off an explosive. Otherwise, it results in some combination of energy exchange and/or energy dissipation.

End result is there is no single equation, but it is a solvable problem.