How to solve this "mechanics" problem?
The question is:
A ship S is moving with constant velocity (-2.5i+6j) = speed of 6.5 km/h. At time 1200, the position vector of S relative to a fixed origin O is (16i+5j). The bearing on which S is moving is 337.4 degrees.
The ship is heading directly towards a submerged rock R. A radar tracking system station calculates that, if S continues on the same course with the same speed, it will hit R at the time 1500. The position vector of R is (8.5i+23j).
The captain maintains S on its course with the same speed until the time 1400. He then changes course so that S moves due north with a constant speed of 5km/h. Assuming that S continues to move with this new constant velocity, find the distance of S from R at the time 1600.
An expression for the position vector of the ship at time 1400 is (11i+17j)
An expression for the position vector of the ship t hours after 1400 is [11i+(17+5t)j]
The time when S will be due east of R is 1312
I always get the position vector of S at time 1600 (11i+37j) and so the distance is 14.22km
However the correct answer includes: position vector of S at time 1600 is (11i+27j) and the distance is 4.72km
I don’t know why I always get the extra 10, or how to get rid of it. Can you please help. Thanks in advance.