Question

A Coast Guard cutter detects an unidentified ship at a

distance of 20.0 km in the direction 15.0° east of north.

The ship is traveling at 26.0 km/h on a course at 40.0° east

of north. The Coast Guard wishes to send a speedboat to

intercept and investigate the vessel. If the speedboat travels

at 50.0 km/h, in what direction should it head? Express the

direction as a compass bearing with respect to due north.

Answer 1

In order to catch other ship the boat must have two components of the velocity in which component perpendicular to line AB will have same magnitude.

A coast guard cutter detects an un-identified ship at a distance of 20.0km.

we choose the x-axis along 20km distance, the y-components of the displacement of the ship and speed of the boat will be.

let t be the time to travelling

then on equating the distances, we have.

the speed of the boat should head with an angle.

15degree + 12.7degree = 27.8degree east of north.