PLEASE HELP FIND GROUND SPEED!! An airplane with an airspeed of 400 mi/hr is flying in the direction 50°, and a 40 mi/hr wind is blowing directly from the west.

Question

An airplane with an airspeed of 400 mi/hr is flying in the direction 50°, and a 40 mi/hr wind is blowing directly from the west. As shown in the figure, these facts may be represented by vectors p and w of magnitudes 400 and 40, respectively. The direction of the resultant p + w gives the true course of the airplane relative to the ground, and the magnitude ||p+w|| is the ground speed of the airplane. Approximate the true course and ground speed. (Round your answers to the nearest whole number.)

True course=53

Ground speed

Answer 1

Tan θ = y÷x

400 sin(40°) ÷ 40+400cos(40°) = 0.7422108817

θ = tan^-1(0.7422108817) = 37°

So, the true course of airplane is 90°-37° = 53°

Ground Speed

= ||p+w||

= √(40+400cos(40°))²+(400 sin(40°))²

^{= 431 miles/hour}