Question 30695
I am hoping that south easterly means SSE --> South south east which means that it has a bearing of 45 degrees.
North to east is 90 degress so 90+45=135degrees
In vector form this forms a oblique triangle:
<pre><b>
N
|500km/h
|
|135 degrees 
 \
  \
   \60km/h
    \
This allows us to use the cosine law:
Letting the unknow be in vector form of ||v+w||
Form cosine law: *[tex ||v+w||=500^2+60^2-2(500*60)cos135]
*[tex ||v+w||=253600+42426.4]
*[tex ||v+w||=296026.4]
||v+w||&#8776; 544
TO find direction use sine law:
*[tex \frac{sin x}{500}=\frac{sin90}{||v+w||}]
*[tex sinx=\frac{500sin90}{544}]
*[tex sinx=\frac{500}{544}]
*[tex sin^-1x=0.91]
x &#8776; 66


<font color = red>Hence, the ground speed of the plane is 544km/h making a direction of 66 degrees.</font>
Paul.