b) When a skydiver (of mass m = 50 kg) drops from a plane, she is immediately subjected to two forces: a constant downwa

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B When A Skydiver Of Mass M 50 Kg Drops From A Plane She Is Immediately Subjected To Two Forces A Constant Downwa 1 (73.73 KiB) Viewed 15 times

b) When a skydiver (of mass m = 50 kg) drops from a plane, she is immediately subjected to two forces: a constant downward force mg = 500 N due to gravity, and an air resistance force proportional to the square of her speed. By Newton's law, the skydiver's speed v satisfies the differential equation du 50- = 500 - - kv² dt where t is time and k is a constant. (i) After a long time (roughly 12 seconds, in real life), the skydiver will reach a terminal (constant) velocity of 80 metres per second. Without solving the given differential equation, determine k. (ii) Solve the given differential equation (using the value of k found in (i)). You should assume that the skydiver is initially at rest, i.e. that v(0) = 0. (iii) Sketch your solution for t≥0.