1) A cave explorer drops a stone from rest into a hole. The speed of sound is 343 m/s in air, and the sound of the stone striking the bottom is heard 1.33 s after the stone is dropped. How deep is the hole?
I did 343 / 1.33. Is this correct?
Physics(Please help) - drwls, Sunday, May 27, 2012 at 12:44am
No. Dividing a speed by a time gives you an acceleration rate. You have to write an equation for the time it takes to hear the sound. That time consists of two terms: stone drop time and sound travel time.
So I would set my problem up as
(13.3 - X/343)^2 = x/1.76
The only thing I am not sure of is how to solve for the x.
let ts be the time for sound to travel up, and td the time to fall to the bottom.
td+ts-1.33seconds
depth= 1/2 g td^2=4.9(1.33ts)^2
also, depth= 343m/s*ts
set these two equal, solve for ts. Notice it is a quadratic. Once you get the ts, solve for deptth
iam trying to find out when a rock drops onto a well 17 seconds later it hits the water how far down is the water level from the top of the well
To solve for the depth of the hole (x), you can rearrange the equation you've written and subsequently solve for x.
Starting with the equation:
(13.3 - x/343)^2 = x/1.76
1. Expand the left-hand side of the equation:
(13.3 - x/343)(13.3 - x/343) = x/1.76
2. Distribute the terms:
(13.3)^2 - 2(13.3)(x/343) + (x/343)^2 = x/1.76
3. Simplify:
176.89 - 26.6x/343 + x^2/117049 = x/1.76
4. Multiply the entire equation by 117049 to eliminate the denominators:
(176.89)(117049) - (26.6x)(342) + (x^2)(625) = (x)(65978)
5. Simplify and bring all terms to one side of the equation:
2071980 - 9136x + 625x^2 = 65978x
6. Rearrange the equation in the form of a quadratic equation:
625x^2 - 9136x + 65978x - 2071980 = 0
7. Combine like terms:
625x^2 + 56842x - 2071980 = 0
Now, you can solve this quadratic equation for x using methods such as factoring, completing the square, or using the quadratic formula.