Question

Einstein and Lorentz, being avid tennis players, play a fast-paced game on a court where they stand 25.0 m from each other. Being very skilled players, they play without a net. The tennis ball has mass 0.0580 kg. You can ignore gravity and assume that the ball travels parallel to the ground as it travels between the two players. Unless otherwise specified, all measurements are made by the two men.Part ALorentz serves the ball at 83.0 m/s . What is the ball's kinetic energy?Part BEinstein slams a return at 1.79×108m/s. What is the ball's kinetic energy?Part CDuring Einstein's return of the ball in part B, a white rabbit runs beside the court in the direction from Einstein to Lorentz. The rabbit has a speed of 2.21×108m/s relative to the two men. What is the speed of the rabbit relative to the ball?Part DWhat does the rabbit measure as the distance from Einstein to Lorentz?Part EHow much time does it take for the rabbit to run 25.0 m , according to the players?Part FThe white rabbit carries a pocket watch. He uses this watch to measure the time (as he sees it) for the distance from Einstein to Lorentz to pass by under him. What time does he measure?

Answer 1

Answer:

A) 199.78 J

B) 9.292x10^14 J

C) 4.2x10^7 m/s

D) 0.65 m

E) 1.13x10^-8 sec

D) 2.94x10^-9 sec

Explanation:

mass of ball = 0.0580 kg

A)

If smashed at v = 83.0 m/s, KE is

KE = 0.5mv^2

= 0.5 x 0.0580 x 83.0^2

= 199.78 J

B) if returned at v = 1.79×10^8 m/s, KE will be

KE = 0.5mv^2

= 0.5 x 0.0580 x (1.79×10^8)^2

= 9.292x10^14 J

C) during Einstein's return, velocity of rabbit relative to players is

Vr = 2.21×108 m/s

Rabbit's velocity relative to ball = 2.21×10^8 - 1.79×10^8

= 4.2x10^7 m/s

D) the rabbit's speed approaches the speed of light so we consider relativistic effect. The rabbit's measured distance is

l = l°( 1 - v^2/c^2)

= 2.5(1 - 2.21/3)

= 2.5 x 0.26

= 0.65 m

E) according to the players, the time taken by the rabbit is

t = d/v = 2.5/ 2.21×10^8

= 1.13x10^-8 sec

F) the time for rabbit as measured by rabbit is relativistic

t = t°( 1 - v^2/c^2)

= 1.13x10^-8 (1 - 2.21/3)

= 1.13x10^-8 x 0.26

= 2.94x10^-9 sec