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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Q: The figure shows a pendulum with length L that makes a maximum angle θ0 with the vertical. Using…

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Q: Situation 3. A stone is shot on a level ground at an angle of 56° with the horizontal with an…

A: Stone is shot at an angle 560 from the ground with an initial velocity 112 m/s

Q: The figure below shows a pendulum with length L that makes a maximum angle with the vertical. +…

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Q: 10. An airplane flying 390 feet per second at an altitude of 5000 feet flew directly over an…

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Q: angular velocity o (in radis) of a pendulum is -0.50 sin 2.01. Find the angular displacement 0 as a…

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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.