Inspired by Arifur Rahman!

Classical Mechanics Level 3

Two astronauts are on the moon, they are 1 1 kilometer apart. One shouts to the other for help. As the astrounats can't communicate in space, the sound needs to be converted into radio signals.

Suppose it takes 5 × 1 0 − 2 5 \times 10^{-2} seconds to convert the signals from sound to radio, and the same time is required to convert the radio waves back to sound. In the case above, the astronaut's sound gets converted to a 100 100 kilohertz wave of wavelength 5 5 centimeters.

To add another complication let's assume that it takes 0.2 0.2 seconds for the astronauts brain to interpret the sound. What is the total time required for the wave to reach the second astronaut?

Now, the second astronaut needs to reach the first astronaut to provide help. He runs with a speed of 2 2 meters per second. Only if he reaches the first astronaut within 10 10 minutes he will be able to help.

Add 0.1 0.1 seconds to the time taken for the wave to reach the second astronaut if he can accomplish the task. Subtract 0.1 0.1 seconds if he cannot accomplish the task. Input your answer accordingly.

Inspiration

0.6 0.5 Data inadequate. None of the above 0.4

Sravanth C. by Sravanth C. , 21, India

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2 solutions

Sravanth C.
May 10, 2015

Here, the frequency of the wave, ν = 100000 H z \nu=100000Hz

Wavelength, λ = 5 c m = 5 100 m = 0.05 m \lambda=5cm=\dfrac{5}{100}m=0.05m

Hence the speed of the wave v = ν × λ = 100000 × 0.05 m / s v=\nu\times\lambda=100000×0.05m/s

= 5000 m / s =\boxed{5000m/s}

Now, the time taken by the wave to travel 1000m = 1000 5000 = 0.2 s =\dfrac{1000}{5000}=\boxed{0.2s}

We also know, according to the question, time taken to transmit and receive the sound = 2 × 5 × 1 0 − 2 = 0.1 s =2×5×10^{-2}=\boxed{0.1s} .

Also the time taken by the second astronauts' brain to interpret the sound wave = 0.2 s =0.2s

Hence the total time taken by the wave to reach the astronaut = 0.2 + 0.1 + 0.2 = 0.5 s =0.2+0.1+0.2=\boxed{0.5s} ( . . . . . . . . ( i ) ) (........(i))

Now, the speed at which the second astronaut is moving towards the first = 2 m / s =2m/s

Distance required = 1000 m =1000m

Therefore the time required for the astronaut to reach the first astronaut = 1000 2 = 500 s =\dfrac{1000}{2}=\boxed{500s}

Max. time within which the astronaut should reach the destination = 10 m i n = 10 × 60 = 600 s =10min=10×60=\boxed{600s} , whicjh means that the astronaut will reach the destination in time, hence we should add 0.1 to ( i ) (i)

Therefore the answer = 0.5 + 0.1 = 0.6 =0.5+0.1=\boxed{\boxed{\boxed{0.6}}}

7 Helpful 0 Interesting 0 Brilliant 0 Confused

For some reason, I took the first astronaut as also needing 0.2 seconds to interpret the sound. Thus is the daily life of the Jake.

Jake Lai - 6 years, 1 month ago

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Hmm . . . . The last sentence sounds weird . . .

Sravanth C. - 6 years, 1 month ago

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Trust me, it's syntactically intact for a didactic fact.

Jake Lai - 6 years, 1 month ago

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@Jake Lai – Na. . . I'm not convinced.

Sravanth C. - 6 years, 1 month ago

in the question it is mentioned 1 megahertz

CH Nikhil - 6 years, 1 month ago

your solution is wrong

CH Nikhil - 6 years, 1 month ago
Suprem S.Nalkund
May 19, 2015

Nice question

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you very much! ⌣ ¨ \huge\ddot\smile

Sravanth C. - 6 years ago

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