Question

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))&gt; 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).1. Find the slope of the path at time t = 4. Show the computations that lead to your answer.2. Find the time when the skier's horizontal position is x = 60.3. Find the acceleration vector of the skier when the skier's horizontal position is x = 60.4. Find the speed of the skier when he is at his maximum height and find his speed in meters/min.5. Find the total distance in meters that the skier travels from t = 0 to t = 15 minutes.

Answer 1

Answer:

Slope of path at time t = 4 is y '(4)/x '(4) = (-15cos(4) + 4cos(4) - 1 + sin(4))/(6 - 2sin(4))

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When horizontal position is 60:

2 + 6t + 2cos(t) = 60

Step-by-step explanation: