Answer to Question #86341 in Mechanics | Relativity for Lucia

Question

a 42km/hr wind blows in the direction 35 degrees south of west, while a helicopter headed toward 55 degrees north of west at 152 km/hr relative to the air. What is the resultant velocity of the helicopter?

Answer 1

The velocity of the wind:

$$v_w=(42 cos 35, -42 cos 35 ) km/hr$$

The velocity of a helicopter relative to the air:

$$v_h = (132 cos 55, 132 sin 55) km/hr$$

The resultant velocity of the helicopter:

$$v_r=v_w+v_h=(42 cos 35+132 cos 55, 132 sin 55 -42 cos 35 ) km/hr$$

$$v_r=132 km/hr$$

Or 132 km/hr 34 degrees north of west.