Question

At a particular time, the distance to Mars is 7.5 x 10¹⁰meters. How long does it take for a radio signal from Mars Pathfinder to be received by NASA on earth?

Answer 1

The radio signal travels at the speed of light, which in a vacuum is approximately
`\(3 * 10^8\)` meters per second takes approximately 4.17 minutes.

Step-by-step explanation:

Given:
The distance to Mars is
`\(7.5 * 10^(10)\)` meters.
The speed of light is
`\(3 * 10^8\)` meters per second.

We can calculate the time it takes for a radio signal to travel this distance by dividing the distance to Mars by the speed of light.

The formula to calculate the time t is:

`\[ t = \frac{\text{distance}}{\text{speed}} \]`

Now we just plug in the values:

`\[ t = (7.5 * 10^(10))/(3 * 10^8) \]`

When we divide
`\(7.5 * 10^(10)\)` by
`\(3 * 10^8\)`, we get:

`\[ t = (7.5)/(3) * 10^(10-8) \]`

`\[ t = 2.5 * 10^2 \]`

So the time taken for the radio signal to travel from Mars to Earth is
`\(2.5 * 10^2\)` seconds.

Converting this to minutes, since there are 60 seconds in a minute, we get:

`\[ 2.5 * 10^2 \text{ seconds} * \frac{1 \text{ minute}}{60 \text{ seconds}} \]`

`\[ 2.5 * 10^2 / 60 \]`

`\[ 2.5 * (10^2)/(60) \]`

`\[ (250)/(60) \]`

`\[ 4.166\ldots \]`

So, it takes approximately 4.17 minutes for a radio signal from the Mars Pathfinder to be received by NASA on Earth.

Answer 2

It would take approximately 250,000 seconds for a radio signal from Mars Pathfinder to be received by NASA on Earth.

Step-by-step explanation:

To find out how long it takes for a radio signal from Mars Pathfinder to be received by NASA on Earth, we need to use the speed of light as a reference. The speed of light is approximately 3 x 10^8 meters per second. Since the distance to Mars is given as 7.5 x 10^10 meters, we can calculate the time it takes for the signal to travel that distance.

Using the formula distance = speed x time, we rearrange the equation to solve for time: time = distance / speed. Plugging in the values, we get:

time = (7.5 x 10^10 meters) / (3 x 10^8 meters per second) = 250,000 seconds.

Therefore, it would take approximately 250,000 seconds for a radio signal from Mars Pathfinder to be received by NASA on Earth.