A watermelon is launched by a catapult with an initial velocity of 89 feet per second and an angle of 61∘ to the horizontal. If the watermelon is launched with an initial height of 9 feet, thus the parametric equations for the watermelon's motion is x(t)=(89cos61∘)t, y(t)=−16t2+(89sin61∘)t+9.  After how many seconds does the watermelon reach its maximum height? (Round your answer to the nearest tenth if necessary.)

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A: Image is attached with detailed solution.

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.