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exam1_fall2009

# exam1_fall2009 - PHY 251 Fall 2009 Exam 1(Thursday October...

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PHY 251 Fall 2009: Exam 1 (Thursday, October 1). 1. While staring out the window, you are somewhat astonished to see a spear go flying past, and you snap a photograph. From your photo you see that it is 2 meter long and tilted up at an angle of 25 from the x direction, and it goes flying past at v x = 1 . 5 × 10 8 m/sec and v y = 0 . What is length, and tilt angle, of the spear in its own inertial reference frame? Answer: Because of relative motion in the x direction, we see a contracted version of the spear’s length. There’s no motion in the y direction, so we see the true length in that direc- tion. That is, we see x = x 0 and y = y 0 and from that we can say r = x 2 + y 2 and tan( θ ) = y /x . Note that γ = 1 / radicalBig 1 β 2 = 1 / radicalBigg 1 ( 1 . 5 × 10 8 3 × 10 8 ) 2 = 1 / radicalBigg 1 ( 1 2 ) 2 = 1 / radicalBig 3 / 4 = 2 / 3 = 1 . 155 . We can relate these to dimensions in the spear’s frame of reference as follows: r 0 = radicalBig x 2 0 + y 2 0 = radicalBig x 2 γ 2 + y 2 = radicalBig [2cos(25 )] 2 (1 . 155) 2 + [2sin(25

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