Question

A man dropped a dime in a wishing well , he heard it 5 sec later ..Find distance traveled if moving at 10 m/s 2

Answer 1

The distance traveled is 109.58 m

Step-by-step 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;

`x = \frac{-b\pm \sqrt{b^(2)-4\cdot a\cdot c}}{2\cdot a}`

Which gives;

`t_1 = \frac{-344\pm \sqrt{344^(2)-4* 5* (-1720)}}{2* 5}`

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.