This problem is not from school but it is something I'm trying to solve for a computer program. Given an exact speed S I am trying to find find a position equation using time where I can randomize x and y, and then solve for z.
So far this is what I have:
I'm representing a vector in 3 space by < Vx(t), Vy(t), Vz(t)>
the magnitude of a velocity vector is the speed which = sqrt( Vx(t)2 + Vy(t)2 + Vz(t)2)
because my velocity is constant
S = sqrt( Vx(t)2 + Vy(t)2 + Vz(t)2)
Now I need to put this into a parametric form so solving for the Vx(t) I get
Vx(t) = sqrt( S2 - Vy(t)2 - Vz(t)2 )
Now here is the hard part. This is what I can't do. I just started calc3 and calc2 did not teach me this so here it is: I need the equation for Rx(t) so the obvious thing to do is to take the integral/anti-derivative.
so....
the integral of Vx(t) = Rx(t) = integral sqrt( S2 - Vy(t)2 - Vz(t)2 ) dt = ?
If I have done anything wrong in my problem thus far or if there is another way of doing this please let me know. Also, If you don't understand anything also tell me and I'll try to clarify. I sent a picture of the formula I'm trying to solve if that helps.
So far this is what I have:
I'm representing a vector in 3 space by < Vx(t), Vy(t), Vz(t)>
the magnitude of a velocity vector is the speed which = sqrt( Vx(t)2 + Vy(t)2 + Vz(t)2)
because my velocity is constant
S = sqrt( Vx(t)2 + Vy(t)2 + Vz(t)2)
Now I need to put this into a parametric form so solving for the Vx(t) I get
Vx(t) = sqrt( S2 - Vy(t)2 - Vz(t)2 )
Now here is the hard part. This is what I can't do. I just started calc3 and calc2 did not teach me this so here it is: I need the equation for Rx(t) so the obvious thing to do is to take the integral/anti-derivative.
so....
the integral of Vx(t) = Rx(t) = integral sqrt( S2 - Vy(t)2 - Vz(t)2 ) dt = ?
If I have done anything wrong in my problem thus far or if there is another way of doing this please let me know. Also, If you don't understand anything also tell me and I'll try to clarify. I sent a picture of the formula I'm trying to solve if that helps.
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