Question

A ship A steaming due north at 10 km per hour is sighted at noon. A second ship B in direction due east and 12 km away is steaming northeast at 5 km per hour. Calculate to the nearest degree the bearing of A from B at 12:15 pm.

Answer 1

To find the bearing of ship A from ship B at 12:15 pm, we need to consider the velocities and directions of both ships. Ship A is steaming due north at 10 km/h, while ship B is steaming northeast at 5 km/h. By using vector addition and the arctan function, the bearing of A from B is calculated to be 73.74 degrees.

Step-by-step explanation:

To find the bearing of ship A from ship B at 12:15 pm, we need to consider the velocity and direction of both ships. Ship A is steaming due north at 10 km/h, which means its velocity is directly upwards. Ship B, on the other hand, is steaming northeast at 5 km/h.

We can calculate the resulting velocity of ship B by using vector addition. The velocity of ship A can be represented by the vector (0 km/h, 10 km/h) and the velocity of ship B can be represented by the vector (5 km/h, 5 km/h).

Adding these vectors together gives us a resultant vector of (5 km/h, 15 km/h). To find the bearing, we can use the arctan function, which is the inverse tangent function. Therefore, arctan(15/5) gives us the result of 73.74 degrees.