202122: applications, Rolle's theorem, grad. EVE Online is a space-based multi-player game, where players use spaceships to engage in combat, industry, explorationand other activities.a) A player is seeking to travel from her current position in a combat arena to theexit gate. The gate is located inside a cloud of gas, which is bounded by a plane:inside this gas, the ship's speed increases from v₁ to v₂. The diagram belowexplains the situation: she will travel from point A to point C by way of pointB. (You may assume that any changes in speed or direction are instantaneous.)с02T =01X - XXi. Explain why the time taken for the player to get to the exit gate is given byY-yx² + y² √(x − x)² + (Y− y)²+V1V2ii. The player wishes to choose point B on the boundary in order to minimisethe total travel time from point A to point C. Use calculus to show that,for this quickest trajectory, the angle 02 depends on 0₁ according to therelationsin 01V1sin 02V2

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Answered: 202122: applications, Rolle's theorem,…

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