He was there when it all began.
Guarding fiercely the old mouth of the Singapore River, he witnessed the meteoric rise and rise of a glorious nation, as modern skyscrapers rose around him, and old warehouses turned into trendy dance clubs, and students began using calculators in their PSLE, while he dutifully maintained law and order in the river by keeping errant sampans in line with his lethal water spout.
As the years went by, however, he slowly felt forgotten by the relentless pace of progress, as the sampans themselves got transformed into tour boats.
More spouts of resignation were to follow when he learnt that younger and mightier clones (including a Godzilla-like monster that can shoot laser beams from its eyes) were recruited across the island to perform his job, and that the only occasions he was ever mentioned were in jokes involving drunk patrons of pubs and clubs.
But still he kept his dignity in defiance of the changing times, and continued his balancing act in a forgotten corner of Singapore to spray his jet of water with pride, even when they cruelly deprived him of his daily sunrise viewing by building a huge bridge across his face.
In the end, the straw that broke the Merlion’s back came when he was relocated against his will to another location. The loss of his spiritual home, combined with his inability to get used to being photographed and molested left, right and center by daily hordes of kawaii teeny trigger-happy tourists in this ironically spanking new location, finally pushed him over the edge.
And so, on a dark sunless day, he turned (as far as he could) to take a final look at his son (and discovered to his further horror that he hasn’t really grown all these years), before closing his eyes and imploring the heavens to put him out of his misery.
A passing 雷公 aka Lightning God heard his plea, and proceeded to plot his target coordinates …
The Merlion’s water spout follows a path defined by the curve y2 = 4x + 64, y > 0 and the lightning bolt (that travels in a straight line) is poised to strike the Merlion’s head at the point (0, 8), which lies on the path of the water spout.
On the seaward side, a group of tourists are snapping photos of the Merlion’s front from a Singapore River Cruise boat, with a line of vision that’s tangent to the water sprout at (0, 8).
On the landward side, a group of kawaii teeny Japanese tourists are snapping photos of the Merlion’s rear with an angle of elevation of 60° from them to the point (0, 8).
Given that the straight line lightning bolt is so powerful that it can travel through the Merlion’s head and harm anything beyond, find the range of possible values of its gradient so that the tourists will be safe from harm.
While this should ultimately be a straightforward enough problem involving the special y2 curve that made its way to the new A-Maths Syllabus last year, please make sure you sketch out the right graphs in this scenario in order to prevent the 雷公 from making any careless mistake that can lead to tragic consequences for the innocent tourists!