Question

A spacecraft with proper length 200 m travels at speed of 0.2c relative to an inertial frame of reference S. A small ball rolls inside the spacecraft with a velocity $u' = 0.14c$ in the positive $x$ direction relative to the spacecraft. a. What is the ball's speed as measured by an observer in frame S? Give answer in units of c. 0.33 b. How much time will it take to the ball to cross the whole spacecraft (end to end) according to an observer in frame S? Give answer in microseconds ($1 \mu s = 10^{-6} s$). c. What is the distance the ball rolled (relative to frame S). Give answer in km.

          A spacecraft with proper length 200 m travels at speed of 0.2c relative to an inertial frame of reference S. A small ball rolls inside the spacecraft with a velocity $u' = 0.14c$ in the positive $x$ direction relative to the spacecraft.
a. What is the ball's speed as measured by an observer in frame S? Give answer in units of c.
0.33
b. How much time will it take to the ball to cross the whole spacecraft (end to end) according to an observer in frame S? Give answer in microseconds ($1 \mu s = 10^{-6} s$).
c. What is the distance the ball rolled (relative to frame S). Give answer in km.

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A spacecraft with proper length 200 m travels at speed of 0.2c relative to an inertial frame of reference S. A small ball rolls inside the spacecraft with a velocity u' = 0.14c in the positive x direction relative to the spacecraft.
a. What is the ball's speed as measured by an observer in frame S? Give answer in units of c.
0.33
b. How much time will it take to the ball to cross the whole spacecraft (end to end) according to an observer in frame S? Give answer in microseconds (1 μ s = 10^-6 s).
c. What is the distance the ball rolled (relative to frame S). Give answer in km.

Added by Jennifer H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Penny Riley

08/15/2023

Step 1

This can be found using the relativistic velocity addition formula: \[v = \frac{u' + v'}{1 + \frac{u'v'}{c^2}}\] where: - \(u' = 0.14c\) (velocity of the ball relative to the spacecraft) - \(v' = 0.2c\) (velocity of the spacecraft relative to frame S) Show more…

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A spacecraft with proper length 200m travels at speed of 0.2c relative to an inertial frame of reference S. A small ball rolls inside the spacecraft with a velocity u^(')=0.14c in the positive x direction relative to the spacecraft. a. What is the ball's speed as measured by an observer in frame S ? Give answer in units of c. b. How much time will it take to the ball to cross the whole spacecraft (end to end) according to an observer in frame S ? Give answer in microseconds (1mu s=10^(-6)s). c. What is the distance the ball rolled (relative to frame S ). Give answer in km. A spacecraft with proper length 200 m travels at speed of 0.2c relative to an inertial frame of reference the spacecraft a.What is the ball's speed as measured by an observer in frame S? Give answer in units of c 0.331 b.How much time will it take to the ball to cross the whole spacecraft(end to end according to an observer in frame S?Give answer in microseconds1s=10-6s c.What is the distance the ball rolled(relative to frame S).Give answer in km

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