A soccer ball is kicked from ground level with (x, y)-coordinates (85, 20) on the soccer field shown in  Figure 11 and with an initial velocity v₀ = 10i − 5j + 25k ft/s. Assume an acceleration of 32 ft/s² due to gravity and that the goal net has a height of 8 ft and a total width of 24 ft.

(a) Determine the position function that gives the position of the ball t seconds after it is hit.

(b) Does the ball go in the goal before hitting the ground? Explain why or why not.

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105 ft 105 ft 165 ft x 165 ft 12 12