Question

In: Physics

1. While watching a storm, you decide to use your audio an electronic skills to build...

1. While watching a storm, you decide to use your audio an electronic skills to build an apparatus to measure the distance from a lightning strike using a light detector and a microphone. When the light detector picks up a lightning flash, the apparatus then measures the time until the microphone picks up the thunder. On your first trial with this apparatus, it seems to work! It measures a time of 6.93 second between the lightning and thunder. Take the speed of sound to be 343 m/s and calculate the distance to the location of the lightning strike in kilometers.

2. Feeling ambitious by your lightning-distance apparatus, you decide to use a similar technique that measures the distance from the top of a well to the bottom by dropping a rock and listening for the sound of the water splash. You assume that the time it takes for the splash to reach the microphone is much less than the time it takes for the rock to hit the water. If the time from it takes to record a sound from the moment the rock is dropped is 2.31, then how deep is the well? Express your answer in meters.

Solutions

Expert Solution

1. Assuming that the light is instantaneously visible to you since the speed of the light is very fast. The time taken by the sound to cover this distance is 6.93 seconds. So, the distance where the lightning struck can be given as:

2. Let, the height of the well be h, the time taken by the rock to reach the bottom of the lake be t1. So, using motion equation, the value of h can be given as:

where, s is the distance travelled by the rock

u is the initial velocity of the rock = 0 m/s

t is the time taken by the rock to reach the bottom

a is the acceleration of the rock, given by g = 9.8 m/s^₂

...............................(i)

Also, the time taken by the sound to travel back to the microphone can be given as:

.................(ii)

Also, we know that the total time is:

Equating (i) and (ii):

Substituting the value of Time:

Since time can only be positive, the solution will be:

Substituting the value of t in (i) to get the height of the well:

PLEASE RATE.

genius_generous answered 1 year ago

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