Problem $4$: $(10$ pts$)$ An airplane with $m=80,000kg$ experiences a thrust of $160$ kN $.$ The

airplane is initially at rest.

$($a$)$ Find the energy required to reach take$-$off velocity $(60\frac{m}{s}.$ Neglect air

resistance, neglect friction from the rolling tires, and assume that the

thrust is constant. $($Hint: You may calculate this is two ways: find the

distance required and determine the energy, or use the kinetic energy

difference.$)$

$($b$)$ What is the minimum runway length, assuming a safety factor of $2,$ to

assure take$-$off? Compare this value to the length of the shorter runway

at Tallahassee Airport $($TLH$).$

Problem $5$: $(10$ pts$)$ A cylinder fitted with a piston contains $5$ kg of R $-134$a superheated

vapor at $1000$ kPa and $140C.$ The cylinder is cooled at constant pressure

until the R$-134$a has a liquid fraction of $25\%.$ Calculate the work done in this

process. Use tables D$1-3$ in Schaum's $4$th ed$.$ to find the volume of R$-134$a$.$