# Math

Trigonometry Problem:

The good ship Bravery is 30 km due west of the good ship Courageous. The Bravery sets out on a bearing of 030° at a speed of 20km/hr. The Courageous sets out on a bearing of 345° at a speed of 25km/hr. Will the ships collide?

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1. The "x" distance between the ships starts at 30 km and diminishes at a rate 20 sin30 + 25 sin 15 = 10 + 6.47 = 16.47 km/hr. The x separation distance becomes zero at 30/16.47 = 1.821 hr.

At that time, the y coordinate of Bravery has increased by 20 cos30*1.821 = 31.54 km
and the y coordinate of the Courageous has increased by 25 cos15 *1.821 = 43.97 km

They do not collide. For a collision to occur, changes in y coordinates would have to be the same when the x difference is zero, since they start out with the same y value.

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posted by drwls

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