Respuesta :
Answer:
The distance traveled is 109.58 m
Explanation:
The Speed of sound in air = 344 m/s
Let the time in which the dime dropped by the man reach an impact in the well = t₁
Let the time in which the sound travel from the well to the man = t₂
Then
1/2× 10 × t₁² = 344 × t₂ which gives;
5 × t₁² = 344 × t₂.........................(1)
Also the total time before the man heard the dime = t₁ + t₂ = 5
Therefore;
t₂ = 5 - t₁
Substituting the value of t₂ in equation (1), we have;
5 × t₁² = 344 × (5 - t₁)
5·t₁² + 344·t₁ - 1720 = 0
Using the quadratic formula, we have;
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
Which gives;
[tex]t_1 = \dfrac{-344\pm \sqrt{344^{2}-4\times 5\times (-1720)}}{2\times 5}[/tex]
t₁ = 4.68 s or -73.48 s
Therefore, with the positive value for t₁ = 4.68 s, we have
The distance = 1/2× 10 × 4.68² = 109.58 m
The distance traveled = 109.58 m.
