Answer
(a) The diver makes $3.02$ turns while falling 10.0 meters in a tuck position.
(b) The diver makes $1.56$ turns while falling 10.0 meters in a pike position.
Work Step by Step
(a) We can find the time it takes to fall 10.0 meters:
$y = \frac{1}{2}gt^2$
$t = \sqrt{\frac{2y}{g}}$
$t = \sqrt{\frac{(2)(10.0~m)}{9.80~m/s^2}}$
$t = 1.43~s$
We can find the angular speed when in a tuck position:
$I~\omega = L$
$\omega = \frac{L}{I}$
$\omega = \frac{106~kg~m^2/s}{8.0~kg~m^2}$
$\omega = 13.25~rad/s$
We can find the number of turns the diver makes while falling 10.0 meters:
$(13.25~rad/s)(\frac{1~rev}{2\pi~rad})(1.43~s) = 3.02~rev$
The diver makes $3.02$ turns while falling 10.0 meters in a tuck position.
(b) We can find the angular speed when in a pike position:
$I~\omega = L$
$\omega = \frac{L}{I}$
$\omega = \frac{106~kg~m^2/s}{15.5~kg~m^2}$
$\omega = 6.84~rad/s$
We can find the number of turns the diver makes while falling 10.0 meters:
$(6.84~rad/s)(\frac{1~rev}{2\pi~rad})(1.43~s) = 1.56~rev$
The diver makes $1.56$ turns while falling 10.0 meters in a pike position.
