A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.15. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = 170(1 − e−0.15t) where t is measured in seconds (s) and v(t) is measured in feet per second (ft/s). (a) Find the initial velocity of the sky diver.  ft/s (b) Find the velocity after 5 s and after 10 s. (Round your answers to one decimal place.) after 5 s       ft/s after 10 s       ft/s (c) Draw a graph of the velocity function v(t).         (d) The maximum velocity of a falling object with wind resistance is called its terminal velocity. From the graph in part (c) find the terminal velocity of this sky diver. (Round your answer to the nearest whole number.)  ft/s

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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.