(Ill) A particle of mass m is projected horizontally at

Chapter , Problem 100

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(Ill) A particle of mass m is projected horizontally at arelativistic speed v0 in the +x direction. There is a constantdownward force F acting on the particle. Using the definitionof relativistic momentum p = 7m \ and Newtons secondlaw F = d\>/dt, (a) show that the x and y components ofthe velocity of the particle at time t are given by% ( 0 = Poc/(m2c2 + Po + F2t2) 2vy(t) = ~Fct/(m2c2 + Po + F2t2)iwhere p0 is the initial momentum of the particle,(b) Assume the particle is an electron (ra = 9.11 X 10 31 kg),with v0 = 0.50 c and F = 1.00 X 10-15N. Calculate thevalues of vx and vy of the electron as a function of time tfrom t = 0 to t = 5.00 /as in intervals of 0.05 /jls. Graphthe values to show how the velocity components changewith time during this interval, (c) Is the path parabolic, asit would be in classical mechanics (Sections 3-7 and 3-8)?Explain.