Question

During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light, that is, $3 \times {10^8}m{s^{ - 1}}$.

Answer 1

Hint – Here we will proceed by using the formula for speed to find out the distance of the spaceship from the ground station.
Formula used - $Speed = \dfrac{{Dis\tan cetravelled}}{{Timetaken}}$

Complete step-by-step answer:

Here it is given that,
$3 \times {10^8}m{s^{ - 1}}$
Given, the signal travels at the speed of light,
$v = 3 \times {10^8}m{s^{ - 1}}$
We know that,
Time taken by the signal to reach the ground $ = 5\min $
 $ = 5 \times 60\sec $
$ = 300\sec $
Let the distance of the spaceship from the ground station be $D m$
We know,
$Speed = \dfrac{{Dis\tan cetravelled}}{{Timetaken}}$
$
   \Rightarrow v = \dfrac{d}{t} \\
   \Rightarrow D = v \times t \\
 $
$
   = 3 \times {10^8} \times 300 \\
   = 900 \times {10^8} \\
   = 9 \times 100 \times {10^8} \\
   = 9 \times {10^{8 + 2}} \\
   = 9 \times {10^{10}}m \\
 $
So the distance of the spaceship from the ground is $9 \times {10^{10}}$ meters.

Note – Whenever we come up with this type of question, where we are asked to find out whether the distance or speed. Then we first write the formula, after writing the formula we will put the values. After solving that we will find out the asked quantity (here distance of a spaceship from a ground station).