An elevator is descending with uniform acceleration. To determine...

Let the downward acceleration of the elevator be $a$.

The acceleration of the freely falling coin is $g = 32 \text{ ft/s}^2$ downwards.

The relative acceleration of the coin with respect to the elevator is $a_{rel} = g - a$ downwards.

Since the coin is dropped at the instant the elevator starts, the initial relative velocity of the coin is $u_{rel} = 0$.

The relative displacement of the coin is $s_{rel} = 6 \text{ ft}$ and the time taken is $t = 1 \text{ s}$.

Using the equation of kinematics for relative motion:

$s_{rel} = u_{rel}t + \dfrac{1}{2}a_{rel}t^2$

Substituting the values:

$6 = 0 + \dfrac{1}{2}(32 - a)(1)^2$

$12 = 32 - a$

$a = 20 \text{ ft/s}^2$