Question

Please fill in all the blanks with correct answer (include explanation where possible), thankyou

Brandishing your mathematical skills, you find a summer job helping out with the 2020 New Years Eve fireworks display on Sydney Harbour 503m The Sydney Harbour Bridge The lower arch of the Sydney Harbour Bridge is 503 metres in width and 118 metres high. It is also a parabola. If the zeros of the parabola are at 0 and 503, then the vertex is at the point (503/2,118 Hence the equation of the parabola is y- -(472/2530097x"2+(472x/503) We will use this equation in the next few questions. Suppose a flaming ball is set to fire from [0,0] and flxed 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 a and y co- ordinates can be specified as a function of t in seconds, as z(t) t)t(t-6) 118 da: Note: We are assuming a constant ar-velocity, ie di should be constant The distance travelled by the ball at time u seconds is given by the formula da dt dt dt Hence after 4 seconds the ball has travelled (to the nearest metre) Numbermetres Note: you will probably want to use Maple of WolframAlpha to calculate this integral. The speed of the flaming ball is the rate of change in distance travelled. Hence the speed of the flare at time seconds is o) tL After 5 seconds the ball is moving at a speed of Number metres per second (to the nearest integer). The initial speed of the ball is Number Recall: that the equation describing the lower arch of the bridge is y The average height above launch level of the ball is (to the nearest metre) Number Recall the formula for the speed at time u seconds is given by metres per second (to the nearest integer) 472 503118 metres e(u) _ 읊.(")-y@())AR()) To accommodate even more fireworks in the 2020 schedule, the artistic director requires that the ball must now take only 3seconds to exactly follow the trajectory of the lower arch. Hence the new initial speed is (to the nearest integer) (o)-Numbermetres per second

Answer 1

Page No. hmt 503m 6 503 118 9 9 503 6 236t t 236 dt 9 ce Teacher's Signoture

503, 12 23 6 2 236 236 9x2 36x2 -23 6 236 3K23 2 36 503) 36 x 2 T) な1-1151.6.6 262 6 teor 3 6x 2

9 ー11511662620虫144 a l , ơD143 New V(5) 36 1653 154 432, 12 98-88 m LA 2 gnitiaL Abend 603 1+236 - 11 smls

x (t)503t da dt 503 3 185 2