The Fastest Way Uphill

A survey drone maps a low hill. With $x$ and $y$ measured in kilometres, the height of the ground above sea level is

$h(x,\,y) = x^2 y + 5\sin(xy)$

measured in metres. The angle inside the sine is in radians.

A hiker stands at the point

$P = \left(2,\; \frac{\pi}{3}\right)$

From $P$ she may step in any horizontal direction she likes. Exactly one of those directions makes the ground rise faster than every other.

Stepping in that best direction, at what rate does her height increase? Give the rate in metres of climb per kilometre travelled.

Round your answer to 2 decimal places.