Question

3. At its closest approach to Earth, Mars is 57.50 million kilometers away. How long in minutes) would a radio signal sent from a future manned mission to Mars take to travel to Earth? (distance = speed x time)

Answer 1

Answer:-

Given:-

Distance between Earth and Mars (d) = 57.50 million kilometers

As we know that

1 million kilometers = 1000000 kilometers = 1000000 km

then

57.50 million kilometers = 57.50 $\times$ 1000000 km

57.50 million kilometers = 57500000‬ km

Also we know that

1 km = 1000 m

then

57500000‬ km = 57500000‬ $\times$ 1000 m

57500000‬ km =  57500000‬000 m

So

Distance between Earth and Mars (d) = 57500000‬000 m = 575 $\times$ 10⁸ m

time (t) =?

Since we know that radio signal is electromagnetic radiation therefore its velocity or speed is equal to the speed of light therefore

speed of radio signal (v) = 3.0 $\times$ 10⁸ m / sec

So according to the formula

speed (v) = distance(d) / time(t)

or

time(t) = distance(d) / speed (v)

therefore

time(t) = Distance between Earth and Mars (d) / speed of radio signal (v)

time(t) = 575 $\times$ 10⁸ m / 3.0 $\times$ 10⁸ m / sec

time(t) = 191.67 sec

Since we know that

60 second = 1 minute

1 second = 1 / 60 minute

then

191.67 sec = 191.67 $\times$ 1 / 60 minute

191.67 sec = 3.19 minute

So 3.19 minutes would radio signal sent from a future manned mission to Mars take to travel to Earth.