A parachutist falls under gravity and the drag on the chute is known to have an air resistance which is proportional to the square of the velocity v and given by kv2 per unit mass. According to Newton’s Law of Motion the velocity of the parachutist satisfies the differential equation
dv/dt = g - kv^2
where g is a gravitational constant. Find the velocity of the particle at any time t subject to the initial condition that v=0 at t=0. Hence confirm that the velocity of the particle tends to the terminal velocity.
Im finding it tricky to differentiate the dv/g-kv^2 bit
It's hard to read what you have written there. I recommend you look at one of the threads on "latex". You can see the code for any Latex on this board by clicking it.
Yes, you can write so, integrating,
Now multiply both sides by and take the exponential of each side to get
Multiply both sides by and multiply on the right so you have
and isolate the "v" terms