what is the true speed of the plane, and what is the true ground speed of this plane?

label Algebra
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A pilot knows that his destination is due straight north and that there is a crosswind of 50 miles per hour in the direction of South 45degrees West. If he starts the plane in the direction of North 30 degrees East, What would the plane speed have to be in order to reach his destination? Furthermore, what is the true sped of the plane?

Jun 24th, 2015

Thank you for the opportunity to help you with your question!

We must have V*sin30 = 50*sin45

V = 50*sqrt(2) = 70.71 mph

 the true speed is 70.71 cos 30 - 50*cos45 = 25.88 mph

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 24th, 2015

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