# Thread: First-order ODE Word Problem (physics-related)

1. ## First-order ODE Word Problem (physics-related)

This is for my DE class and I can't seem to figure it out (probably because my physics is a bit rusty).

Anyway:

An object of mass 100 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy of force 1/40 times the weight (w = mg) of the object is pushing the object up. Also, water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10N-sec/m. Find the equation of motion of the object.

2. Originally Posted by BlazingFire
This is for my DE class and I can't seem to figure it out (probably because my physics is a bit rusty).

Anyway:

An object of mass 100 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy of force 1/40 times the weight (w = mg) of the object is pushing the object up. Also, water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10N-sec/m. Find the equation of motion of the object.
let the downward direction be positive, g = 10 m/s^2 ...

$F_{net} = mg - \frac{mg}{40} - 10v$

$m\frac{dv}{dt} = \frac{39}{40}mg - 10v$

$\frac{dv}{dt} = 9.75 - 0.1v$

go for it ...