A hot-air balloon rises vertically from the ground so that its height after t s is given by the following function. h =  1 2t2 +  1 2t ft where (0 ≤ t ≤ 60) (a) What is the height (in ft) of the balloon at the end of 49 sec?  ft (b) What is the average velocity (in ft/sec) of the balloon between t = 0 and t = 49?  ft/sec (c) What is the velocity at time t? v(t) =

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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.