1. Understand the Physics

* Free Fall: The brick is in free fall, meaning the only force acting on it is gravity.

* Acceleration due to Gravity: The acceleration due to gravity is constant and downward, denoted by 'g' (approximately -9.8 m/s²).

* Vertical Motion: We're dealing with vertical motion, so we'll use the appropriate kinematic equations.

2. Set Up the Problem

* Initial Velocity (v₀): 2.60 m/s (upward, so positive)

* Initial Position (y₀): 100.0 m (height of the building)

* Final Position (y): 0 m (ground level)

* Acceleration (a): -9.8 m/s² (downward, so negative)

* Time (t): We need to find this.

3. Choose the Right Equation

We can use the following kinematic equation:

y = y₀ + v₀t + (1/2)at²

4. Plug in the Values and Solve for 't'

0 = 100 + 2.6t + (1/2)(-9.8)t²

Simplifying the equation:

4.9t² - 2.6t - 100 = 0

This is a quadratic equation. We can solve for 't' using the quadratic formula:

t = [-b ± √(b² - 4ac)] / 2a

Where:

* a = 4.9

* b = -2.6

* c = -100

Plugging in the values and solving, we get two solutions for 't':

* t ≈ 5.07 seconds

* t ≈ -4.04 seconds

5. Choose the Correct Answer

We discard the negative solution because time cannot be negative. Therefore, the brick takes approximately 5.07 seconds to land on the ground.