Factorise the denominator as a difference of two squares, then apply partial fractions.
Hi. I have trouble integrating the following problem.
The equation is basically with the condition when t = 0, v = 50m/s
I know this is a separable DE, so rearranaging it becomes
Now I have trouble integrating the left side. Trig substitution doesn't work, so it seems like it'll end up being logs. Any help? Thanks.
I think I'm doing this wrong, because the values I can when I substitute time is really wrong.
When t = 0, v = 52m/s
Substituting this back
Solving for v
Let
g = 9.8
m = 140
b = 110
When I anything other than t = 0 as the value for t, the value of v gets really close to 3.53, which is the value of
What did I do wrong?
I don't know how to help any further. When I try for a value of the constant I keep betting imaginary numbers. (See here.) As all other numbers in the problem should be arbitrary I have to conclude your value of b = 110 is far too large. I have been trying to find typical values of b to compare, but have so far been unsuccessful. The integral is correct, but I can't get any further than that.
-Dan
I'm thinking this over again. Your object is already traveling faster than the terminal speed at t = 0. All problems of this type I have seen start with the object falling from rest. For some reason this is throwing the equation off. I'll look into it and get back to you when (if!) I solve it.
I guess the different forms can be useful! Thank you for saving me hours of work on this.
(sighs) Now I'm going to have to figure out why one solution worked and the other didn't.
I'm going to bed.
-Dan
Thanks for all your hard work.
@topsquark
This is not a problem from a textbook. I'm trying to model someone falling, but has reached terminal velocity already, hence when t = 0, v = 50. I wanna know his speed 2 seconds after he releases his parachute at t = 0.
The value for k is from the drag equation,
p is 1.22 (density of air)
Cd = 2 (large drag for a parachute)
A = 100m^2 (area of the parachute)
The fact you experts are having trouble with this is making me doubt if I'm doing this question correctly.
I tried Prove It's solution, and I got strange values. Here's Wolfram's solution
solve 140/2sqrt(150920) ln|((sqrt (1372) - 50sqrt(110))(sqrt(1372) + sqrt (110) v))/((sqrt (1372) + 50sqrt(110))(sqrt(1372) -