Question

A 3250-kg aircraft takes 12.5 min to achieve its cruising

altitudeof 10.0 km and cruising speed of 850 km/h. If the
plane'sengines deliver on average, 1500 hp of power during this
time, whatis the efficiency of the engines?

Answer 1

effeciency n = = 49%

Step-by-step explanation:

given data:

mass of aircraft 3250 kg

power P = 1500 hp = 1118549.81 watt

time = 12.5 min

h = 10 km = 10,000 m

v =85 km/h = 236.11 m/s

`n = (P_0)/(P)`

`P_o = (total\ energy)/(t) = ( kinetic \energy + gravitational\ energy)/(t)`

kinetic energy
`= (1)/(2) mv^2  =(1)/(2) 3250* 236 = 90590389.66 kg m^2/s^2`

kinetic energy
`= 90590389.66 kg m^2/s^2`

gravitational energy
`= mgh = 3250*9.8*10000 = 315500000.00  kg m^2/s^2`

total energy
`= 90590389.66 +315500000.00 = 409091242.28 kg m^2/s^2`

`P_o =(409091242.28)/(750) = 545454.99 j/s`

`effeciency\ n = (P_o)/(P) = (545454.99)/(1118549.81) = 0.49`

effeciency n = = 49%