A ship leaves the island of Guam and sails a distance 295km at an angle 35.0 north of west.

Question

a:In which direction must it now head so that its resultant displacement will be 100km directly east of Guam? (Express your answer as an angle measured south of east)
b:How far must it sail so that its resultant displacement will be 100km directly east of Guam?

Answer 1

If it started at O (0,0), then after sailing NW, it arrives at P(-295 cos 35°, 295 sin 35°)

Now we want to arrive at point Q= (100,0)

SO, use the law of cosines to get the distance PQ: PQ² = 295² + 100² - 295*100*cos(180-35)

Now, use the law of sines to get the angle OPQ:

sin 145°/PQ = sin OPQ/100

Now, the heading is 55° + OPQ° east of south