Question

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A hockey puck is sliding on the smooth ice surface of a skating rink as shown in the figure above.

The figure shows the puck’s position on the ice surface at a sequence of equally spaced times t₀, t₁, t₂, t₃ and t₄. The x axis shown is parallel to the rink’s length and the y axis to its width. The marks along the axes are spaced 1 meter apart as are the successive positions of the puck. The unseen z axis points straight up out of the page.

a) Make a list of the objects in the puck’s surroundings that interact significantly with it during the time interval between t₀ and t₄ and explain briefly why you think they do.

b) Draw the arrow on your white board figure representing , the position vector of the puck relative to the coordinate system’s origin, at time $Y7UWOIiuwowErL7Z1CvRnEwAAAABJRU5ErkJggg=$. Do the same for the puck’s positions vectors at time $k0m+4zCRTSLaYtQAAAABJRU5ErkJggg==$ and at time .

c) Draw the arrow representing the puck’s displacement vector during the time interval from $Y7UWOIiuwowErL7Z1CvRnEwAAAABJRU5ErkJggg=$ to $k0m+4zCRTSLaYtQAAAABJRU5ErkJggg==$. We use the symbol $xxoQddsrPiGhRxoAAAAABJRU5ErkJggg==$ to represent changes in a quantity like the time or the position of the puck. For the time interval $Y7UWOIiuwowErL7Z1CvRnEwAAAABJRU5ErkJggg=$ to $Y7UWOIiuwowErL7Z1CvRnEwAAAABJRU5ErkJggg=$, we say that the change in the time is, the final or later time minus the initial or earlier time. Similarly, we use the symbol to represent the displacement vector you drew since , the puck’s final position vector minus its initial position vector.

d) Draw the arrow representing the puck’s displacement$lJWn6aZtAAAAABJRU5ErkJggg==$.

e) What are the components of the puck’s position vectors at times$Y7UWOIiuwowErL7Z1CvRnEwAAAABJRU5ErkJggg=$,$k0m+4zCRTSLaYtQAAAABJRU5ErkJggg==$ and .

f) If the time intervals $xJdAAAAABJRU5ErkJggg==$ and are 2 seconds, what are the components of the puck’s average velocity during each of those intervals?

g) In this physical situation how do you think the puck’s average velocity vector for the interval $xJdAAAAABJRU5ErkJggg==$ compares to the puck’s instantaneous velocity at times $Y7UWOIiuwowErL7Z1CvRnEwAAAABJRU5ErkJggg=$, $k0m+4zCRTSLaYtQAAAABJRU5ErkJggg==$ and ?

Answer 1

I have marked position vectors for dispacements

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