right but I am wondering about that if. What if a is the square root of cos2θ+C for some C>2? wouldn't the equation 1-a2=b2still hold for b = sqrt(sin2θ-C)? And a is no longer equal to cos θ for any θ.
Ah okay so b is a complex number and since the question wanted real solutions I have not...
Doing a past paper where long story short I have a set of equations and I have to prove the variables are equal to some trig function. Namely:
a^2 + c^2 = b^2 + d^2 = 1
ad - bc = ab + cd = 0
Now I know that sin^2 + cos^2 = 1 and that sin(A+B)=sinAcosB + cosAsinB, etc
and the...
Not sure where to post this.
I'm trying to write my dissertation, and both the examiners and I would prefer it if I used latex for the required notation. The frustrating thing is that even though I do know how to produce latex code, I don't know how to save it into a format that the computer...
integrating:
t=arctan(((-c^1/2)/((b-a)^1/2))v)/(b-a)^1/2(-c^1/2)
rearranging:
v=(((b-a)^1/2)/(-c^1/2))tan((b-a)^1/2)(-c^1/2)t
sorry about the horrible presentation I don't know how to use LaTeX.
The -c^1/2 makes me a little uneasy but I've used the tan form of the integral as it's...
Homework Statement
A vehicle of mass m experiences a constant frictional resistance ma and air resistance proportional to the square of its speed. It can exert a constant propelling force mb and attain a maximum speed V Show that, starting from rest, it can attain the speed V/2 in the time...
Homework Statement
A particle of constant mass moves one dimensionally under the influence of a restoring force, proportional to the displacement from the origin, and a damping (resistive) force propportional to the velocity. Write down an appropriate equation of motion for the particle...
^ I'll get back to that one later.
I've started out by trying to differentiate V(x)?
I've got V'(x) = (1/1+x^2)((2x^2/1+x^2) - 1)
Ignoring non-real solutions this leaves x = 1.
Where do I go from there? Do I differentiate again?
dv/dt(m0+(mt-m0/T))+v(mT-m0/t)=-(m0+(mT-m0/T))g-c(mT-m0/T)
How do I go about solving that? General solution and particular integral?
I'll look back over my differential equations, but can you show me the steps from here?
Well.. from this point the propellant force dissapears...
That comes out as reaction= (mT-m0)(c/T + dv/dt)
so the whole thing is Fnet=dv/dt(mT-m0)+c/T(mT-m0)+(m0+((mT-m0)/T))g
yes
Yes.
Yes.
right
I'm still not getting it :(
I'll keep working at this. If I do figure it out I'll make a post saying so.
yes. I've got r'(t) in the question. It's:
(-t^(1/2)sin((t^2)/2) - 1/2t^(-3/2)cos((t^2)/2)i + (t^(1/2)cos((t^2)/2) - 1/2t^(-3/2)sin((t^2)/2)j
The expression for |r'|(t) looks truly horrible though, I think I'm missing a trick somewhere.