# Distance, Time, and Temperature question

• Nathan J
The person who did it took it a bit too far and made it complicated.In summary, a rock is thrown down a well with an initial velocity of 2.10 m/s and is heard striking the bottom of the well 4.22 seconds later. The velocity of the rock just before it hits the bottom of the well is 41.0 m/s. Using g = 9.8 m/s^2, the depth of the well can be found using the formula d=vt, with a time of 4.22 seconds and a velocity of 41.0 m/s, resulting in a depth of approximately 87.5 meters. The time it takes for the rock to hit the bottom of the well

#### Nathan J

A person throws a rock down a well with an initial velocity of 2.10 m/s. The sound of the rock striking the bottom of the well is heard 4.22 seconds after the rock is thrown down. If the velocity of the rock just before it hits the bottom of the well is 41.0 m/s.

What is:
a) The depth of the well
b) The time it takes for the rock to hit the bottom of the well
c) The temperature of the air in the well

DID I DO THIS RIGHT? CHECK MY WORK ON IMAGE.

g = 9.8 m/s ^2
V1 = 2.10 m/s

## Homework Equations

V2 ^2 = V1^2 + 2gd
d=vt

## The Attempt at a Solution

On picture![/B]

#### Attachments

• EDE9D143-670F-4FEE-A9B2-2713406C2249.jpeg
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First, the question is impractical. Drag would likely overwhelm the accuracy of it as a way of finding the temperature.

Are you told to use 9.8 for g? The arithmetic might be a bit sensitive to the values. I would use 9.81.
Either way, I would certainly keep an extra digit through the calculations.

For part b, it would be better to work more directly with the given data than with intermediate results, i.e. use v=u+at. It also avoids quadratics.

Not sure what happened towards the end of part b. You found the time of the fall, then appear to have used that as if it were the time for the sound to come up. But you got a reasonable answer for sound speed, so this was probably an error in copying out your working.

Other than that, all looks fine.

haruspex said:
The arithmetic might be a bit sensitive to the values. I would use 9.81.
I would say that depends on the location of the well...

haruspex
It is just a basic grade 11 question, it isn’t supposed to be too complicated