Problem $4$

a$.$ Scientist at NASA observed an immense cloud of rotating gas and dust contracted under the influence of gravity to form the Earth and in the process rotational kinetic energy increased. This causes an increase in rotational kinetic energy of the Earth now than did the cloud of gas and dust from which it formed. Explain using relevant equation where did this energy come from.

$[4$ points$]$

b$.$ A marine biologist working at the Baltimore Habour observes a squid resting underwater, preparing to propel itself away from a predator by ejecting water from its body. The squid, weighing $5\mathrm{.}00$ kg $,$ ejects $0\mathrm{.}250$ kg of water at a speed of $\backslash (10\mathrm{.}0\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ relative to its body. This quick burst of water helps the squid move, but its motion is slowed by the water's resistance $($a frictional force of $5\mathrm{.}00$ N $).$ Determine

i$.$ The recoil velocity of the squid if the ejection is done at $0\mathrm{.}100$ s

ii$.$ Energy lost to work done against friction.