Question

An airplane is moving at 120 m/s at the angle of 10 degree with x axis, through a 30 m/s cross wind blowing at angle of 260 degree with x axis. determine the resultant velocity of the airplane.


ans 20m​

Answer 1

Explanation:

airplane is moving at 120m/s at an angle of 10° with x axis

Horizontal Speed = 120 Cos 10°

Vertical speed = 120 Sin 10

wind blowing 30 m/s at angle of 260°with x axis.

=> Horizontal Speed = 30 Cos 260° = -30Sin10°

Vertical speed = 30 Sin 260° = -30Cos10°

Net horizontal Speed = 120 Cos 10° - 30Sin10°

Net Vertical Speed = 120 Sin 10° - 30Cos10°

Net velocity = √ (120 Cos 10° - 30Sin10° )² + ( 120 Sin 10° - 30Cos10° )²

= √ (120²Cos²10° + 30²Sin²10 - 2*120*30Cos10°Sin10° + 120²Sin²10° + 30²Cos²10 - 2*120*30Cos10°Sin10° )

= √ (120²(Cos²10° + Sin²10° )+ 30²(Sin²10 + Cos²10) - 2*120*30Sin20° )

= √ (120² + 30² - 2*120*30Sin20° )

= √ (120² + 30² - 2*120*30Sin20° )

= 20 m/s