A man drops a rock into a well. (a) the man hears the sound of the splash 2.40 s after he releases the rock from rest. the speed of sound in air (at the ambient temperature) is 336 m/s. how far below the top of the well is the surface of the water? (b) what if? if the travel time for the sound is ignored, what percentage error is introduced when the depth of the well is calculated?

Question

06-08-2017
Physics

contestada

A man drops a rock into a well. (a) the man hears the sound of the splash 2.40 s after he releases the rock from rest. the speed of sound in air (at the ambient temperature) is 336 m/s. how far below the top of the well is the surface of the water? (b) what if? if the travel time for the sound is ignored, what percentage error is introduced when the depth of the well is calculated?

Respuesta :

Otras preguntas

PLEASE HELP!! The next question refers to the following paragraph. Select the transition that best fits the blank. The kite festival once marked the arrival

A researcher employs an IV × PV design to examine attitudes toward cheating. She presents freshmen from a private university with a written account describing a

Viral-infected human cells often send out special proteins that serve as an early warning system to uninfected cells. In response, the uninfected cells develop

When Josh was dropped off at preschool on the very first day of class, he was quite upset. He cried for a long time and would not play with the other children.

a:b=3, m:n=2:5. Find a/m:b/m

A force that causes mass movement is called a distance b. gravity C. weight d none of the above Please select the best answer from the choices provided OOO

Organizations have built-in mechanisms—like their selection processes and formalized regulations—to produce stability. When an organization is confronted with c

Craig earns extra money as a lifeguard he earns $37 for 4 hours and $64.75 for 7 hours. Identify the constant of proportionality and write an equation for the p

6. If a person pushes a cart with a force of 40 N and it accelerates at 0.5 m/s2, what is the mass of the cart? a. 80N b. 80 kg C. 20 N d. 20 kg

Аноним Аноним · Answer 1 · 2017-08-15T00:40:59+02:00

Part (a)
Let h = depth of water surface from the top of the well, m

Because the stone is dropped, its initial velocity is zero.
Let t₁ = time for the stone to drop, s
Then
h = (1/2)*(9.8 m/s²)*(t₁ s)²
t₁ = √(h/4.9) s = 0.4518√h s

The velocity of sound is 336 m/s.
The time for the sound wave to travel from the water surface to the top of the well is
t₂ = h/336 m/s

Because the time before the sound is heard is 2.4 s, therefore
t₁ + t₂ = 2.4
0.45181√h + h/336 = 2.4
Multiply through by 336.
151.8082√h + h = 806.4
h - 806.4 = -151.8082√h
h² - 1612.8h + 6.5028 x 10⁵ = 2.3046 x 10⁴h
h² - 2.4659 x 10⁴h + 6.5028 x 10⁵ = 0

Solve with the quadratic formula.
h = 0.5[2.4659 x 10⁴ +/- 2.4606 x 10⁴]
= 24632 m or 26.5 m

Test the two answers.
When h = 24632,
t₁ = 0.4518√(24632) = 70.9 s (Not acceptable)
When h = 26.5 m,
t₁ = 0.4518√(26.5) = 2.3258 s, t₂ = 26.5/336 = 0.0789 s,
t₁+t₂ = 2.4 s (CORRECT)

Answer: h = 26.5 m

Part (b)
If travel time for the sound is ignored, then
0.4518√h = 2.4
h = (2.4/0.45118)² = 28.2 m
The percent error is 100*[(28.2 - 26.5)/26.5] = 6.42%

Answer: The error is 6.4%