Problem $4$: $(10pts)$ 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$).$