What is the work done by the engines?

Question

After a small take off, a 50 ton airliner climbs from sea level to an altitude of 8000 m while int he same time acceleration from 100m/s to 250 m/s.    Assume the total drag force on the airplane remains constant at  50kN and that the length traveled along its trajectory is 200 km. Note: Assume aerodynamic drag forces behaves exactly like kinetic friction.

B.)  A small bat catches an insect in flight.  To calculate the velocity of the bat AFTER the capture one should use which of the following?

the conservation of energy
the conservation of momentum
both
either one or
information about the angle at which they collide

Can someone work out the first problem and explain it to me step by step 
and also explain the second problem.  Thanks!

BP · Accepted Answer

A) 
m = 500000kg
h = 8000m
v = delta v = 150 m/s (250-100)
Wk = kinetic energy
Wp = potential energy
A = work done

A = Wk + Wp = mvv/2 + mgh = ...

B) the conservation of momentum
This is because you are interested in velocity (a vector with length and direction). If you would use energies, you would lose information about direction and could only calculate speed.

What is the work done by the engines?

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