# Math Help - I don't understand!

1. ## I don't understand!

A 3250-kg aircraft takes 12.5 min to achieve its cruising altitude of 10.0 km and cruising speed of 850 km/h. If the plane's engines deliver, on average, 1500 hp of power during this time, what is the efficiency of the engines (neglecting air resistance)?

2. Originally Posted by babygirl
A 3250-kg aircraft takes 12.5 min to achieve its cruising altitude of 10.0 km and cruising speed of 850 km/h. If the plane's engines deliver, on average, 1500 hp of power during this time, what is the efficiency of the engines (neglecting air resistance)?
This is a question of how much work the airplane has done vs. how much work the engines have put out.

Work the airplane has done. The total work done is equal to the change in energy. I'm assuming the plane was originally stationary and on the ground. So v0 = 0 m/s and set the gravitational potential energy equal to zero on the ground for convenience. (V0 = 0 J). Then $W_{Plane} = \Delta E = K + V = (1/2)mv^2 + mgh$.

Work done by the engines. You are given that the engines put out an average power of 1500 hp over 12.5 min. $W_{Engine} = P_{ave} \Delta t$.

Efficiency is then: $\frac{W_{Engine} - W_{Plane}}{W_{Engine}} \times 100 \%$

-Dan