b) An arrow is shot straight upward from the ground with an initial velocity of 10 ms. The air resistance is equal to ku g, where v is the velocity of the arrow, k is a constant and g is the gravitational constant. The differential equation is given by dv TM dr -kv – 9. where r is the displacement of the arrow at time t which is taken as positive in the upward direction. Given that g 9.8 ms 2 and k = 0.05, i. Find the expression of the motion in terms of v and r. ii. Find the maximum height attained by the arrow. UTM UTM

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