Suppose a flaming ball is set to fire from [0, 0] and fixed to the rail of the lower arch of the Sydney Harbour Bridge (ie the trajectory of the ball follows the rail). The ball must reach the point [503, 0] in exactly 6 seconds. The x and y co-ordinates can be specified as a function of t in seconds, as • x(t) = • y(t) = 118 9 -t(t - 6). dx Note: We are assuming a constant x-velocity, ie should be constant. dt The distance travelled by the ball at time u seconds is given by the formula 2 dx dy -N√(G)*³- )*- 2 dt. dt dt s(u) = = + Hence after 5 seconds the ball has travelled (to the nearest metre) 수 Note: you will probably want to use Maple of WolframAlpha to calculate this integral. metres.

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