FINAL ASSIGNMENT - QUESTION 4 4. (a) Determine the (shortest) distance between the straight line 1: 1=2+3, y=3-4. 1=241. teR. and the plane P: 2r+ 3y + 6: = 33. (b) When a skydiver (of mass m = 70 kg) drops from a plane, she is immediately subjected to two forces: a constant downward force my = 700 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 70- = 700 - ko- where f is time and & is a constant. (i) After a long time (roughly 12 seconds, in real life), the skydiver will reach a terminal (constant) velocity of 60 metres per second. Without solving the given differential equation, determine k. (ii) Solve the given differential equation (using the value of & found in (i)). You should assume that the skydiver is initially at rest, i.e. that "(0) = 0. (iii) Sketch your solution for f > 0