Question

An airplane is traveling at a speed of 240 miles/hour with a bearing of 110°. The wind velocity is 56 miles/hour at a bearing of 325°. What are the plane's actual speed and direction angle?
PLEASE HELP

Answer 1

Answer:

The actual speed of the plane is 196.77 miles/hour and it is flying at a bearing of 9.4 degrees

Step-by-step explanation:

First of all, we put all the given information on a diagram as shown in the attached picture.

In order to find the resultant velocity, we use cosine rule in triangle OAB as shown below.

$x^{2}=240^2+56^2-2*240*56cos(35)\\x^{2}=57600+3136-22018.81\\x^{2}=38717.19\\x=196.77$

Now, for finding the direction of the actual speed, we use sine rule in triangle OAB as shown below.

$\frac{sin(O)}{240}=\frac{sin(35)}{196.77}\\sin(O)=\frac{240\cdot sin(35)}{196.77}\\Sin(O)=0.6996\\O=44.40^{0}$

Therefore, the actual speed of the plane is 196.77 miles/hour and it is flying at a bearing of 44.40-35 = 9.4 degrees.