Question

A woman dropped a dime in a wishing well , she heard it 30 sec later ..Find velocity on impact while moving at 9.8 m/s 2

Answer 1

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±

$t_1 = \dfrac{-344\pm \sqrt{344^{2}-4\times 4.9 \times 10320}}{2\times 4.9}$

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.