2. Galilean relativity You are the center on a hockey team and Franois is the le

Question

2. Galilean relativity You are the center on a hockey team and Franois is the left wing. After the face off, which you won, you are both heading towards the opposing team?s goal. You both leave from the exact center of the ice at the same time. You have the puck and head directly towards the goal along the x axis with a velocity of magnitude v1, while Franois heads towards the same goal at an angle theta, above to the x axis, with a velocity of magnitude v2. The situation is shown in the figure below. Suddenly, your path to the goal is blocked while Franois remains open. Figure 1: Problem 2 (a) In your reference frame, at what angle, relative to the x-axis, do you have to shoot to pass the puck make the pass to Franois. Give your answer in terms of v1, v2, and theta. (b) What is the minimum velocity, in your reference frame, with which you have to shoot the puck to Franois so that if the rink were infinitely big he would get the pass eventually? (c) The magnitude of your velocity, v1, is 4 m/s, while Francois?s is 5 m/s. Also, theta is 36.7 degrees. What angle, relative to the x-axis, in you reference frame do you have to use to make the pass?

Explanation / Answer

This question is already been asked before pls go through the following link

https://www.chegg.com/homework-help/questions-and-answers/galilean-relativity-2d-center-hockey-team-francois-left-wing-face-won-re-head-towards-oppo-q4806762

However one can approce this problem as below:

In my frame of reference the x & y component of velocity of Francois is

Vx = v1 – v2 cos()   and   Vy = v2 sin()

Let us suppose that the pass happened after time t, Therefore the relative distance travelled by Francois is [v1 – v2cos()]t in x-direction and v2sin() t in y-direction.

The angle at which Francois is tan() = [v2sin() t] / [{v1 – v2cos()}t ]

Therefore,    = tan-1[ v2sin() / {v1 – v2cos()} ]

This is the angle at which Francois is from you, but he is still moving when I pass the ball. So the angle will the smaller than this for Francois to receive the ball after time t’ which is time taken by the ball to reach Francois.

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