Directions (or bearings) on Earth are measured in degrees, running from zero to 360 degrees, clockwise, starting with 0 degrees being due North. So due East for example, is 90 degrees, due South 180 degrees, and Northwest is 315 degrees.

You are swinging a rock clockwise (looking from above) around your head and you are trying to hit a broomstick 15 feet due east of you. The rock moves in a circle of a radius of 3 feet around your head. When you release your sling the rock will continue to move along the tangent to the circle through its position at the time of the release. When you release the rock, what direction in degrees is the sling pointing?

Ignore the vertical motion of the rock.

1 answer

Make a sketch.
Your rock will travel in a circle whose equation is
x^2 + y^2= 9
you must release it at a point P(x,y) so that it reaches a point (15,0)
Anyway, we have right-angled triangle , (at the point of release, the angle is 90° between radius and tangent.
let the bearing angle be Ø,
sinØ = 3/15
Ø = 11.54°