# maths

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The relationship between the vertical height and the horizontal distance of a ball thrown at 45 degree is given by the equation y = x - x^2/50, where y is the vertical height and x is the horizontal distance. (a) Find the maximum vertical height reached. (b) Find the horizontal distance travelled.

• maths -

(a) Take the derivative and solve for x when y' is 0. Evaluate y at that value.

(b) Solve the equation for x when y is 0.

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Alternatively, note that a ballistic curve of that form (quadratic) is symmetric around the maxima/minima and use the solution of one to solve the other.

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