Part of a cross-country skier's path can be described with the vector function r = <2 + 6t 2 cos(t), (15 − t)(1 sin(t))> for 0 ≤ t ≤ 15 minutes, with x and y measured in meters.

The derivatives of these functions are given by x′(t) = 6 − 2sin(t) and y′(t) = −15cos(t) + tcos(t) − 1 + sin(t).

Find the slope of the path at time t = 4. Show the computations that lead to your answer.

Find the time when the skier's horizontal position is x = 60.

Find the acceleration vector of the skier when the skier's horizontal position is x = 60.

Find the speed of the skier when he is at his maximum height and find his speed in meters/min.

Find the total distance in meters that the skier travels from t = 0 to t = 15 minutes.