An airplane is moving at 120m/s at an angle of 10° with x axis, through a 30 m/s cross wind blowing at angle of 260°with x axis. Determine the resultant velocity of the airplane
Answers
the resultant velocity of the airplane = 113.3 m/s
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° )
= 113.3 m/s
the resultant velocity of the airplane = 113.3 m/s
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