Question 1

Paper 2Medium4 marks

A trolley moves at constant velocity in the +x+x direction relative to the ground. Let SS be the ground frame and S′S' the frame of the trolley. The Galilean transformations are x′=x−vtx'=x-vt and t′=tt'=t where vv is the velocity of S′S' relative to SS

(a)

Using the transformations for the positions of an object at two different times, show that its velocity u′u' measured in S′S' is related to its velocity uu measured in SS by u′=u−vu'=u-v

[2]
(b)

A puck moves at +2.5 m s−1+2.5\ \mathrm{m\,s^{-1}} relative to the ground while the trolley moves at +4.0 m s−1+4.0\ \mathrm{m\,s^{-1}} relative to the ground. Determine the puck’s velocity relative to the trolley, including its direction.

[2]

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