calorimetry
Sep20-09, 02:57 PM
1. The problem statement, all variables and given/known data
If vector r(t) is not 0, show that d/dt |r(t)| = (1/|r(t)|) r(t)dot r'(t).
The last part is the dot product of r(t) and r'(t).
2. Relevant equations
The hint given was that |r(t)|^2 = r(t) dot r(t)
3. The attempt at a solution
Not sure where to begin, but I thought that |r(t)| is the length or magnitude of the vector r(t), thus its derivative is zero. If this is correct, then I also need to prove that the right side = zero.
If vector r(t) is not 0, show that d/dt |r(t)| = (1/|r(t)|) r(t)dot r'(t).
The last part is the dot product of r(t) and r'(t).
2. Relevant equations
The hint given was that |r(t)|^2 = r(t) dot r(t)
3. The attempt at a solution
Not sure where to begin, but I thought that |r(t)| is the length or magnitude of the vector r(t), thus its derivative is zero. If this is correct, then I also need to prove that the right side = zero.