Re: Mechanical Mathematics

Quote:

Originally Posted by

**weijing85** A diver of mass 60 kg, on entering water with an initial velocity of 15.35 ms^{-1, }experiences a force of resistance, due to the water opposing motion, of magnitude 180v Newtons, where v is the velocity of the diver in ms^{-1}. In addition to the force of gravity, the diver also experiences a constant upward buoyancy force of 720 N. Take the origin of motion to be at the surface of the water. The magnitude g of the acceleration due to gravity can be taken as 10 ms^{-1. }

Calculate the maximum depth, in metres, the diver will submerge. Give your answer to 3 decimal places.

The answer is 4.41. Can anyone show me the workings? :'(

Rgds, Bruce

I'm going to set upward to be the positive (vertical) direction.

As always we set $\displaystyle \Sigma F = ma$

Just about everything is pointed upward save the weight.

$\displaystyle \Sigma F = -w + B + R = -mg + 720 + 180v = ma$

From here you can calculate the acceleration. You've got an initial velocity and an acceleration. How do you find the greatest depth from here?

-Dan

Re: Mechanical Mathematics

Hi dan, can give me some more hints...i still cant get it.

Re: Mechanical Mathematics

find the acceleration (deceleration) as indicated by -Dan and then apply the Uniform Decelaration formula to find the total space (depth) travelled..

Re: Mechanical Mathematics

I calculated the acceleration is 5. Am i right?