**Answer:**

The marble will take 8.813 seconds to hit the ground.

**Explanation:**

The marble will fall according to this motion equation: y(final) = y(initial) + v(initial)×t + 1/2×a×t×t

y(final)=0 m, the marble's final position in relation to the ground

y(initial)=381 m, the marble's initial position in relation to the ground

v(initial)=0 m/s (meters per second), the marble's initial velocity (speed with direction) when fall first begins

t=? seconds, this is the amount of time that passes while falling, the variable in this problem

a=-9.81 m/s/s, the rate at which the velocity of the marble changes, acceleration. On Earth, neglecting friction, acceleration is a constant at negative 9.81 meters per second squared

Plug the values into the equation: 0= 381 + 0t + 1/2(-9.81)(t)(t)

Subtract 381 from both sides and disregard 0t because it has no value and no longer matters: -381= 1/2(-9.81)(t)(t)

Multiply out the equation: -381= -4.905(t)(t)

Divide both sides by -4.905 to isolate the variable: 77.676=(t)(t)

Find the square root of both sides: t=8.813 seconds