Two diamonds begin a free fall from rest and from the same height 1 second apart. a. Provide an expression for the position as a function of time for the first particle.
b. Provide an expression for the position as a function of time for the second particle
c. How long after the first diamond begins to fall will the two diamonds be 25 m apart?

Explanation:

let t be time since the second diamond is released

a) y = ½g(t + 1)²

b) y' = ½g(t)²

c)

25 = ½g(t + 1)² - ½gt²

25 = ½g(t² + 2t + 1) - ½gt²

25 = ½gt² + gt + ½g - ½gt²

25 = g(t + ½)

t + ½ = 25 / g

t = (25 / g) - ½

t = (25 / 9.8) - ½

t = 2.05102... ≈ 2.1 s

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