Final answer:
To find the bearing of ship A from ship B, we can calculate the velocity of ship B relative to ship A and find the angle between the velocity vector and the north direction.
Step-by-step explanation:
To find the bearing of ship A from ship B, we can use vector addition. Let's calculate the velocity of ship B relative to ship A. Ship B is steaming northeast at 5 km/hr, which can be represented as a vector of magnitude 5 km/hr and direction of 45 degrees east of north.
Ship A is moving due north at 10 km/hr. The velocity of ship B relative to ship A is the vector subtraction of the velocity of ship A from the velocity of ship B. This can be calculated as:
Velocity of B relative to A = Velocity of B - Velocity of A = 5 km/hr at 45 degrees east of north - 10 km/hr at 0 degrees north.
By taking the difference:
Velocity of B relative to A = 5 km/hr at 45 degrees east of north - 10 km/hr at 0 degrees north = 5 km/hr at 45 degrees east of north - 10 km/hr at 90 degrees east of north
= -5 km/hr at 45 degrees east of north - 10 km/hr at 0 degrees east of north
= -15 km/hr at 45 degrees east of north
The bearing is the angle between the velocity vector of B relative to A and the north direction. Therefore, the bearing of A from B at 12:15 pm is:
Bearing = 360 degrees - 45 degrees = 315 degrees.