(a) Find the escape velocity \(d r / d \tau\) of a particle of mass \(m\) starting from rest at radius \(r_{0}=4 G M / c^{2}\) in a Schwarzschild spacetime of mass \(M\), where \(\tau\) is read on the particle's own clock.

(b) Then find the escape velocity \(d r / d \tau\) of the particle, starting at rest from the same point, where now \(\tau\) is read on a clock that remains at rest at \(r_{0}\).