The range R of a projectile fired from the origin over horizontal ground is the distance from the origin to the point of impact. If the projectile is fired with an initial velocity y0 at an angle a with the horizontal, then in Chapter 12 we find that R =y02/g sin 2a, where g is the downward acceleration due to gravity. Find the angle a for which the range R is the largest possible.

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A: Explained below

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A: Please refer to the image below.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.