Question

A woman is 1.6 m tall and has a mass of 55 kg. She moves past an observer with the direction of the motion parallel to her height. The observer measures her relativistic momentum to have a magnitude of 2.7 × 10¹⁰ kg·m/s. What does the observer measure for her height?

Answer 1

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we know relativistic momentum, P_rel = mo*v/sqrt(1 - (v/c)^2)

sqrt(1 - (v/c)^2) = mo*v/P_real

sqrt(1 - (v/c)^2) = 55*v/(2.7*10^10)

sqrt(1 - (v/c)^2) = 2.037037*10^-9*V

1 - (V/C)^2 = 4.14952*10^-18*V^2

1 = ( 4.14952*10^-18 + 1/C^2)*V^2

1 = ( 4.14952*10^-18 + 1/(9*10^16))*V^2

V = 1/SQRT(4.14952*10^-18 + 1/(9*10^16))

= 2.55985*10^8 m/s

now use Length constraction euquation, L = Lo*sqrt(1 - (v/c)^2)

= 1.6*sqrt(1 - (2.55985/3)^2)

= 0.8343 m

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