Chapter 16.1, Problem 14SSC

To determine

The distance from the Earth to the Moon.

Answer to Problem 14SSC

The distance from the earth to moon is $\boxed{3.84\times {10}^8\text{m}}$ .

Explanation of Solution

Given:

Time taken by the pulse of light to travel to the moon and again return to the earth is $T=2.562\text{s}$ .

Formula used:

The distance from the earth to the moon is the product of the velocity of the light and the time taken by the light to travel the distance is

  $d=ct$  ...... (1)

Here, $t$ is the time taken by the light and $c$ is the speed of light.

Calculation:

The time taken $\left(t\right)$ by the light to travel from the Earth to the Moon is half of the time taken $\left(T\right)$ by the light to travel to the moon and come back to the earth i.e.

  $t=\frac{T}{2}$  ...... (2)

Substitute 2.562 s for $T$ in equation (1)

  $\begin{array}{l}t=\frac{2.562\text{s}}{2}\\ t=1.28\text{s}\end{array}$

The distance from the earth to the moon is calculated as from equation (1)

Substitute $3.0\times {10}^8\text{m}\cdot {\text{s}}^{\text{-1}}$ for $c$ and $1.28\text{s}$ in equation (1)

  $\begin{array}{l}d=\left(\text{3}{\text{.0×10}}^{\text{8}}\text{m/s}\right)\times \left(1.28\text{s}\right)\\ \boxed{d=3.84\times {10}^8\text{m}}\end{array}$

Conclusion:

Hence, the distance from the earth to moon is $\boxed{3.84\times {10}^8\text{m}}$ .