Answer:
The velocity at impact is 222.2 m/s
Explanation:
The given information are;
The time at which the woman heard the sound of the coin after dropping it into the wishing well = 30 seconds
The average speed of sound in air = 344 m/s
The time in which the dime travel = t₁
The time in which the sound travel = t₂
1/2 × 9.8 × t₁² = 344 × t₂
t₁ + t₂ = 30
4.9·t₁² = 344 × (30 - t₁)
4.9·t₁² + 344·t₁ - 10320 = 0
Which gives -344±
[tex]t_1 = \dfrac{-344\pm \sqrt{344^{2}-4\times 4.9 \times 10320}}{2\times 4.9}[/tex]
t₁ = 22.676 seconds or -92.9 seconds
Therefore the correct natural time is t₁ = 22.676 seconds
The velocity at impact, v = g×t₁ = 9.8 × 22.676 = 222.2 m/s
The velocity at impact= 222.2 m/s.
