1995 Paper 3 Q11

Year: 1995
Paper: 3
Question Number: 11

Course: LFM Pure and Mechanics
Section: Vectors

Difficulty: 1700.0 Banger: 1500.0

vectors relative velocity wind navigation optimisation trigonometry ratio

Problem

A ship is sailing due west at \(V\) knots while a plane, with an airspeed of \(kV\) knots, where \(k>\sqrt{2},\) patrols so that it is always to the north west of the ship. If the wind in the area is blowing from north to south at \(V\) knots and the pilot is instructed to return to the ship every thirty minutes, how long will her outward flight last? Assume that the maximum distance of the plane from the ship during the above patrol was \(d_{w}\) miles. If the air now becomes dead calm, and the pilot's orders are maintained, show that the ratio \(d_{w}/d_{c}\) of \(d_{w}\) to the new maximum distance, \(d_{c}\) miles, of the plane from the ship is \[ \frac{k^{2}-2}{2k(k^{2}-1)}\sqrt{4k^{2}-2}. \]

No solution available for this problem.

Rating Information

Difficulty Rating: 1700.0

Difficulty Comparisons: 0

Banger Rating: 1500.0

Banger Comparisons: 0

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Problem source

A ship is sailing due west at $V$ knots while a plane, with an airspeed
of $kV$ knots, where $k>\sqrt{2},$ patrols so that it is always
to the north west of the ship. If the wind in the area is blowing
from north to south at $V$ knots and the pilot is instructed to return
to the ship every thirty minutes, how long will her outward flight
last? 

Assume that the maximum distance of the plane from the ship during
the above patrol was $d_{w}$ miles. If the air now becomes dead calm,
and the pilot's orders are maintained, show that the ratio $d_{w}/d_{c}$
of $d_{w}$ to the new maximum distance, $d_{c}$ miles, of the plane
from the ship is 
\[
\frac{k^{2}-2}{2k(k^{2}-1)}\sqrt{4k^{2}-2}.
\]

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