Question

a single - from a satellite in space travels to the surface of the earth. a signal takes 0.0812 seconds to reach the surface of the earth. what is the approximate distance, in kilometers, from the satellite to the surface of earth? (note: use 2.998 x 10^8 meters/second for the speed of light. 1,000 meters = 1 kilometers) a. 3,692,118 b. 24,344 c. 2,434 d. 406

Explanation:

Step1: Recall the distance - speed - time formula

The formula is $d = vt$, where $d$ is distance, $v$ is speed and $t$ is time.

Step2: Identify the values of $v$ and $t$

The speed of light $v=2.998\times 10^{8}$ meters per second. The time $t = 0.0812$ seconds.

Step3: Calculate the distance in meters

$d=v\times t=(2.998\times 10^{8})\times0.0812$ meters.
$d = 2.998\times0.0812\times 10^{8}$ meters.
$2.998\times0.0812 = 0.2434376$.
So $d=0.2434376\times 10^{8}$ meters.

Step4: Convert meters to kilometers

Since $1$ kilometer = $1000$ meters or $10^{3}$ meters, to convert the distance from meters to kilometers, we divide by $10^{3}$.
$d=\frac{0.2434376\times 10^{8}}{10^{3}}$ kilometers.
Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $d = 0.2434376\times10^{8 - 3}$ kilometers.
$d=0.2434376\times 10^{5}$ kilometers.
$d = 24343.76\approx24344$ kilometers.

Answer:

b. 24344