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. (b) What is the magnitude of the brick's velocity just before it reaches the ground?

Verified step by step guidance

1. Identify the relevant equations for the problem. Since the brick is in free fall, the only force acting on it is gravity. The equation to use here is the final velocity equation for uniformly accelerated motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
2. Substitute the known values into the equation. The initial velocity u is 0 m/s (since the brick is dropped), the acceleration a is the acceleration due to gravity (approximately 9.81 m/s^2), and the time t is 1.90 seconds.
3. Simplify the equation by multiplying the acceleration due to gravity by the time. This will give you the magnitude of the final velocity just before the brick reaches the ground.
4. Since the direction of the acceleration due to gravity is downwards, the final velocity will also be directed downwards. This means the velocity vector points towards the ground.
5. The magnitude of the velocity is the absolute value of the final velocity calculated. This is the speed of the brick just before impact.

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, and it accelerates downward at a constant rate due to gravity, which is approximately 9.81 m/s² on Earth.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. For free fall, one key equation relates the final velocity (v), initial velocity (u), acceleration (a), and time (t): v = u + at. Since the brick starts from rest (u = 0), the equation simplifies to v = at, allowing us to calculate the final velocity just before impact.

Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, including both speed and direction. In this context, the magnitude of the brick's velocity just before it strikes the ground indicates how fast it is moving downward, which can be calculated using the time of free fall and the acceleration due to gravity.