Problem 9.7

9.7.
First, we need to find the $\gamma$ of the system. At .500 c, we find that
$\gamma = (1 - .5^{2})^{-1/2}$
$\gamma = 1.155$
According to the time dilation equation,
$\Delta t = \gamma \Delta t'$
$\Delta t = (1.155)(.80 sec)$
$\Delta t = .924 s$
Therefore, the pulse rate is given by
$rate = \frac{60 s/min}{.924 sec}$
rate = 64.9 beats per minute.  
At a relative speed of v = .990 c, the factor $\gamma$ increases to
$\gamma = 7.09$
So, the pulse rate decreases to 10.6 beats per minute.