Question

Please please help!! I have these answers- I just need to know HOW to do it!

26. Two planes leave an airport at the same time. One travels on a heading of 78° at a speed of 200 mph. The second plane travels on a heading of 332° at a speed of 300 mph. After 2 hours, what is the distance between the planes and the bearing of the first plane from the second plane?

807.654 mi; 123.571°

27. A man walks 2 miles on a heading of 200° then 3.2 miles on a heading of 102°. How far is the man from his starting point and which direction should he walk to head home?

3.530 mi; 316.133°

Answer 1

Distance trevelled by first plane is D1 = 200×2 =400 miles

In coordinates D1 = 400cos78i + 400sin78 j

= 83.164i +391.26 j miles

Distance trevelled by plane 2 is D2 = 300×2 = 600 miles

In coordinates D2 = 600 cos332 i + 600sin 332j

= 529.77 i - 281.68 j miles

Now D1-D2= -446.603 i +672.94j miles

So magnitude is D = 807.65 miles

And angle = atan ( 672.94÷(-446.603)) = 123.57°

27----

D1 = 2cos200i + 2sin200j

= -1.88i - 0.684 j

D2 =3.2cos102i +3.2sin 102j

= -0.665i +3.13j

So D1+D2 = -2.545i +2.446j

Or D = 3.529 miles

and angle is atan(2.446÷(-2.545) = 136.133° is this his current position

Hence to go home man has to trevel 3.53 miles and in direction 136.133+180 = 316.133°

as 180° means opposite direction