Calculus question related to vectors need help!

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))> 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

Hi John,

As I mention in the video. This is a long, multi-step question. I quickly go through the ideas behind how to solve them, but as we're advised to keep videos under five minutes long, I treated this generally without getting into too much detail. This should give you the information you need to tackle the problem, however.

Please message me if you would like to go into this problem or other similar ones more in depth.