27.13.Set Up:The doctor in the rocket measures his proper length Solve: (a)The person on earth would measure his height to be 1.05 m.(b)This is not a reasonable height for a human.(c)There is no length contraction in a direction perpendicular to the motion and both observers measure the sameheight, 2.00 m.Reflect:The length of an object moving with respect to the observer is shortened in the direction of the motion, soin (a) and (b) the observer on earth measures a shorter height.27.14.Set Up:The scientist at rest on the earth’s surface measures the proper length of the separation between thepoint where the particle is created and the surface of the earth, so The transit time measured in theparticle’s frame is the proper time,Solve: (a)(b)(c)time dilation formula:from The two results agree.27.15.Set Up:The height measured in the earth’s frame is a proper length. The lifetime measured in the muon’sframe is the proper time.
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