A car is travelling up the inclined plane with an inclination of 14^o with a velocity of v = 50 Km/h. The mass of the car is 4 Mg. If mechanical friction and wind resistance are neglected, determine the power developed by the engine if the automobile has an efficiency E = 0.5

1) 263.7 kW
2) 350.5 kW
3) 320.8 kW
4) 450.4 kW

Equation of motion: The force F which is required to maintain the car's constant speed up the slope must be determined first:
S F_x^' = ma_x^'
F - 4(10³)(9.81) sin14^o = 4(10³) 0
F = 9493 N

Power: Here, the speed of the car is
v = (50(10³) m/h)(1 h/3600s) = 13.89 m/s

The power output can be obtained as:
P = F . v = 9493 ( 13.89 ) = 131.85(10³) W
P = 131.85 kW

The required power inout to the engine to provide the above power output is
Power input = power output/E = 131.85/0.5 kW
Power input = 263.71 kW

So the power developed by the engine with an efficiency E(0.5) is 263.7 kW