Question

An airplane is moving at 120 m/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.
AIRPLANE THROUGH WIND
Assignment 2.1
(20 m)​

Answer 1

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 100

Vertical speed 120 Sin 10

Wind blowing 30 m/s at angle of

260 with x axis.

=>Horizontal Speed = 30 Cos 260° = -30 sin 10°

Vertical speed 30 Sin 260° = -30Cos10°

Net horizontal Speed 120 Cos 10°

30Sin10

Net Vertical Speed = 120 Sin 10

30Cos10

Net velocity = v (120 Cos 10°

30Sin10° ? +( 120 Sin 10 30Cos10*)?

=V (120 Cos210 + 30Sin10 -

2120 30Cos10°Sin10° +1203Sin210°+

30 Cos210 - 2"120 30Cos10 Sin10°)

= (120(Cos10°+ Sin210° )+ 30(Sin210

Cos10) 2 120 30Sin20°)

= (1202 + 302 2120 30Sin20°)

= (120 +302 - 2*120 30Sin20°)

= 113.3 m/s

I hope it's helpful for you....