Assume the acceleration of the object is  a(t) = −32  feet per second per second. (Neglect air resistance.) A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 62 feet per second. How high will the ball go?

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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.