[12361236]

Question is here http://postimage.org/image/som50onyv/

2. Relevant equations
F=MA


3. The attempt at a solution

for a) Power = force * speed

for b) Force = Mass * Acceleration
F = m * dv/dt

for c) for maximum velocity, there must be zero drag

i am stuck at D and E, so can anyone help me?

[dantheman1261]

It's not zero drag - the drag force doesn't disappear when you reach terminal velocity (in fact, it's at it's maximum). It's just that you stop accelerating, so...

Also for D, you need (well, a small rearrangement of this. Is this familiar?)

[12361236]

for d) i got that k=50

but am stuck for e) again.
m dv/dt = (80000-50v²)/v

thus m v (dv/dx) = (80000-50v²)/v

and thus 1200v (dv/dx) = (80000-50v²)/v

now do i integrate this to find the answer of part e? i'm kinda lost

[dantheman1261]

My mistake - you're right. Just a minute...

Okay. Divide through by the 1200v. Then you have a separable differential equation. The integral is tough (well, annoying) - but not impossible. Begin by cancelling out the 50, then bring the constant on top out of the integral. Then try partial fractions (with some care!). If you're having trouble with the last part, look at the spoiler:

Spoiler:

Show

The fraction has the same degree in the numerator and denominator. This causes some problems - the fraction is improper. There are a few ways to deal with this, but one is to remember that we must include a constant term when expressing in partial fractions: