This question is challenging and involves the ues of calculus...
a) warm up: for a freely falling object compute the velocity...
b) Now we will include air resistance. Typically are resistance takes the form Fd=-bv...
c)Wreite down Newton's second law, now including the drag force.
d) In contrast to free fall, Newton's second law now has solutions with a=0. Determine the velocity Vt, which satisfies Newton's sceond law with zero acceleration in termss of b, m, and g.
e) Now follow what you did for part a). Write down Newton's second law and use the fact a=dv/dt
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