Understanding the Concepts

* Gravitational Acceleration (g): The acceleration due to gravity on this planet is 36 m/s². This means that the ball's speed increases by 36 meters per second every second it falls.

* Initial Velocity (v₀): The ball is dropped from rest, so its initial velocity is 0 m/s.

* Displacement (Δy): The ball falls 18 meters, so its displacement is -18 meters (negative because it's moving downward).

Using the Kinematic Equation

We can use the following kinematic equation to solve for the time (t):

Δy = v₀t + (1/2)gt²

Plugging in the Values

* Δy = -18 m

* v₀ = 0 m/s

* g = 36 m/s²

-18 = (0)t + (1/2)(36)t²

-18 = 18t²

Solving for Time (t)

1. Divide both sides by 18: -1 = t²

2. Take the square root of both sides: t = 1 second (we discard the negative solution since time cannot be negative)

Answer: It takes 1 second for the ball to reach the ground.