Question

A ship A, steaming in a direction 30° with a steady speed of 12km/h, sight a ship B. The velocity of B relative to A is 10km/h in a direction of the velocity of B. Find the magnitude and direction

Answer 1

Answer on Question #81814 - Physics - Mechanics - Relativity

A ship A, steaming in a direction $30{}^{\circ}$ with a steady speed of $12\mathrm{km / h}$ , sight a ship B. The velocity of B relative to A is $10\mathrm{km / h}$ in a direction of the velocity of B. Find the magnitude and direction

Solution

Let us find the magnitude of the velocity B relative to the sea, knowing that the speed of B relative to A is $10\mathrm{km / h}$ :

$$v _ {\mathrm {B} | \mathrm {A}} = v _ {\mathrm {A}} \cos 3 0 {}^ {\circ} + v _ {\mathrm {B}},$$ $$v _ {\mathrm {B}} = v _ {\mathrm {B} | \mathrm {A}} - v _ {\mathrm {A}} \cos 3 0 {}^ {\circ} = 1 0 - 1 2 \cos 3 0 {}^ {\circ} = - 0. 3 9 \frac {\mathrm {k m}}{\mathrm {h}}.$$

since the ship B moves opposite to A.

Let us find the direction of a ship B relative to A:

$$\beta = 3 0 {}^ {\circ} - 1 8 0 {}^ {\circ} = - 1 5 0 {}^ {\circ}.$$

Answer

-0.39 km/h; -150°.

Answer provided by https://www.AssignmentExpert.com