Alice drops a rock to a well. She hears the splash of the rock 4.1s later. The speed of sound is 340m/s. How deep is the well
Answered on
Given: Speed of sound =340 m/s, time = 4.1 s
Find the depth of the well
Solution:
In order to solve the given problem, we need to follow certain steps. We will ignore air resistance in solving the problem.
Let d = depth of well
a=-g
v=-gt+v_o
s=-1/2gt^2+vot+s_o
We know vo = 0, and s_o = d
We need to calculate s such that t gives us the time it takes for the rock to fall to the bottom, therefore s should be 0
0=-1/2gt^2+d
Solve the formula for t.
t^2 = 2d/g
t=√(2d/g)
Now solve these simultaneous equation:
Let t_a = time for rock sound to reach Alice
Equation 1
4.1-t = t_a
Substitute t:
4.1-√(2d/g) = t_a
Equation 2
340m/s(t_a) = d
t_a = d/340
4.1-√(2d/g)=d/340
solve for d: (g = 9.81 m/s^2)
D = 73.93 meters