Two ships leave port simultaneously. Ship A sails north-west at 30 km/h and ship B sails S 40 degrees W at 30 km/h. Calculate the velocity of ship B relative to the velocity of ship A.
You add them as vectors.
Vbreltoa=velocityb-veloictya AS VECTORS
A = (-21.2,21.2)
B = (-19.3,-23.0)
B-A = (1.9,-44.2)
= 44.2,-87.5° or 44.2km/hr S2.5°E
To calculate the relative velocity of ship B with respect to ship A, we can use vector addition.
Step 1: Convert the given velocity of ship B from polar coordinates to rectangular coordinates.
Ship B is sailing at a speed of 30 km/h at an angle of 40 degrees west of south. In rectangular coordinates, this can be represented as:
Vb = 30 km/h * (sin(40°) i - cos(40°) j)
= -18.96 i - 22.96 j km/h (rounded to two decimal places)
Step 2: Calculate the relative velocity vector by subtracting the velocity vector of ship A from the velocity vector of ship B.
Va = 30 km/h * (cos(45°) i + sin(45°) j)
= 21.21 i + 21.21 j km/h (rounded to two decimal places)
Relative Velocity, Vrel = Vb - Va
= (-18.96 i - 22.96 j) - (21.21 i + 21.21 j) km/h
= (-18.96 - 21.21) i + (-22.96 - 21.21) j km/h
= -40.17 i - 43.17 j km/h (rounded to two decimal places)
Therefore, the velocity of ship B relative to the velocity of ship A is -40.17 km/h in the north-west direction.