The optimal angle, ignoring air resistance, to maximize distance of a thrown or

Question

The optimal angle, ignoring air resistance, to maximize distance of a thrown or launched object is 45 degree, meaning the vertical and horizontal components are in a 1 to 1 ratio. The velocity, v, at which an object is launched has a horizontal component, v_z, and a vertical component, v_y. If an object is thrown with initial velocity v at a 45 degree angle, express the horizontal v_z and the vertical v_y components of velocity as a function of v using the pythagorean formula for a right triangle and the image given above. The physics equation for the distance an object has travelled is given by the function

Explanation / Answer

Since the given triangle is right-isosceles triangle, the hypotenuse = leg x sq.rt(2).

Given, hypotenuse = v, leg = v/sq.rt(2).

Since both vertical vx and horizontal vy are equal to v/sq.rt(2) or v{sqrt(2)}/2.

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