Chapter 26, Problem 11P

(a)

To determine

The time elapsed on the ship.

Answer to Problem 11P

  $\text{2}\text{.7}\text{yr}$ .

Explanation of Solution

Given:

In the Earth frame, the clock on the Enterprise will run slower.

Time is $5.0yr$

Speed is $0.84c$

Formula used:

It is known that,

  $\Delta t=\frac{\Delta t_0}{{\left[1-\left(\frac{v^2}{c^2}\right)\right]}^{\frac{1}{2}}}$

Where,

  $t_0$ is rest time

  $t$ is time

  $v$ is velocity

  $c$ is speed of light, $3.00\times {10}^{8}m/s$

Calculation:

Calculate the elapsed time on the ship from: $\Delta t=\frac{\Delta t_0}{{\left[1-\left(\frac{v^2}{c^2}\right)\right]}^{\frac{1}{2}}}$

  $5.0yr=\frac{\Delta t_0}{{\left[1-{\left(0.84\right)}^2\right]}^{\frac{1}{2}}}$

  $\Delta t_0=2.7yr$

(b)

To determine

The time passed on Earth.

Answer to Problem 11P

  $\text{9}\text{.2}\text{yr}$ .

Explanation of Solution

Given:

In the Earth frame, the clock on the Enterprise will run slower.

Speed is $0.84c$

Rest Time is $5.0yr$

Formula used:

It is known that,

  $\Delta t=\frac{\Delta t_0}{{\left[1-\left(\frac{v^2}{c^2}\right)\right]}^{\frac{1}{2}}}$

Where,

  $t_0$ is rest time

  $t$ is time

  $v$ is velocity

  $c$ is speed of light, $3.00\times {10}^{8}m/s$

Calculation:

Calculate the elapsed time on the ship from: $\Delta t=\frac{\Delta t_0}{{\left[1-\left(\frac{v^2}{c^2}\right)\right]}^{\frac{1}{2}}}$

  $\Delta t=\frac{5.0yr}{{\left[1-{\left(0.84\right)}^2\right]}^{\frac{1}{2}}}=9.2yr$