A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 1.90 s. You may ignore air resistance, so the brick is in free fall. (a) How tall, in meters, is the building?

Verified step by step guidance

1. Identify the given values: initial velocity (u) is 0 m/s since the brick is dropped, time (t) is 1.90 s, and acceleration (a) is approximately 9.81 m/s² due to gravity.
2. Use the kinematic equation for displacement when acceleration is constant: \( s = ut + \frac{1}{2}at^2 \).
3. Substitute the known values into the equation: \( s = 0 \times 1.90 + \frac{1}{2} \times 9.81 \times (1.90)^2 \).
4. Calculate the value inside the parentheses first, then multiply by the acceleration, and finally multiply by 0.5 to account for the time squared term.
5. The result from the calculation will give you the height of the building in meters.

Key Concepts

Free Fall

Free fall refers to the motion of an object under the influence of gravity alone, with no other forces acting on it, such as air resistance. In this scenario, the brick is dropped from rest, meaning its initial velocity is zero. The only force acting on it is gravity, which accelerates the brick downward at approximately 9.81 m/s².

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. For free fall, one key equation relates displacement (height), initial velocity, time, and acceleration: h = v₀t + 0.5at². Here, h is the height, v₀ is the initial velocity (zero in this case), a is the acceleration due to gravity, and t is the time of fall.

Acceleration due to Gravity

Acceleration due to gravity is the rate at which an object accelerates towards the Earth when in free fall, typically denoted as 'g'. On Earth, this value is approximately 9.81 m/s². This means that for every second an object is in free fall, its velocity increases by about 9.81 m/s, which is crucial for calculating the height from which the brick was dropped.