# physics

posted by .

A spelunker (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 3.24 s after the stone is dropped. How deep is the hole?

• physics -

t1 + t2 = 3.24s.
t2 = 3.24 - t1.

t1 = Flight time of stone.
t2 = Travel time of the sound.

d1 = 0.5gt^2 = distance the stone traveled.

d2 = Vt = Distance the sound traveled.

d1 = d2,
0.5*9.8t^2 = 343m/s * t2,
Substitute 3.24 - t1 for t2:
4.9t1^2 = 343 * (3.24 - t1),
4.9t1^2 = 1111.3 - 343t1,
4.91t1^2 + 343t1 - 1111.3 = 0,
Use Quadratic Formula to find t and get:
t1 = 3.10244, and -73.10.
Use the positive value of t.
t1 = 3.10244s = time in flight for stone.

d1 = 0.5 * 9.8 * (3.10244)^2,
d1 = 47.2m = Depth of hole.

## Similar Questions

1. ### physics

A spelunker 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 1.50s after the stone is dropped. How deep is the hole?
2. ### Physics HELP!

A mountaineer estimates the depth of a crevasse by dropping a stone and listening for sound when the stone hits the bottom. The speed of sound in air is 340m/s. If the sound is heard 10s after the stone is dropped, what is the depth …
3. ### physics

A spelunker drops a stone from rest into a hole. The speed of sound is 343m/s in air, and the sound of the stone striking the bottom is heard 1.46s after the stone is dropped. How deep is the hole?
4. ### physics

You drop a stone into a deep well and hear it hit the bottom 1.90 s later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. …
5. ### physics

A spelunker (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 3.87 s after the stone is dropped. How deep is the hole?
6. ### physics

A boy drops a 0.10 kg stone down a 150 m well and listens for the echo. The air temperature is 20°C. How long after the stone is dropped will the boy hear the echo?