# Math Help - Mechanical Mathematics

1. ## Mechanical Mathematics

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

2. ## Re: Mechanical Mathematics

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 $\Sigma F = ma$

Just about everything is pointed upward save the weight.

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

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

3. ## Re: Mechanical Mathematics

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

4. ## 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..

5. ## Re: Mechanical Mathematics

I calculated the acceleration is 5. Am i right?