A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.480 s. Ignore air resistance. Find (a) the height of the tabletop above the floor;

Verified step by step guidance

1. Identify the initial velocity of the book in the vertical direction, which is 0 m/s since the book starts from rest in the vertical direction.
2. Recognize that the only force acting on the book in the vertical direction is gravity. Therefore, use the acceleration due to gravity (approximately 9.81 m/s^2) as the acceleration in the vertical direction.
3. Use the kinematic equation for vertical displacement, \(y = v_{0y}t + \frac{1}{2}a_{y}t^2\), where \(v_{0y}\) is the initial vertical velocity, \(a_{y}\) is the vertical acceleration, and \(t\) is the time.
4. Substitute \(v_{0y} = 0 m/s\), \(a_{y} = 9.81 m/s^2\), and \(t = 0.480 s\) into the equation to solve for \(y\), the height of the tabletop above the floor.
5. Calculate the value of \(y\) using the substituted values to find the height of the tabletop.

Key Concepts

Kinematics

Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this scenario, kinematic equations can be used to relate the initial speed of the book, the time it takes to fall, and the height from which it falls.

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 case, the book is in free fall after it leaves the tabletop, and its motion can be analyzed using the acceleration due to gravity, which is approximately 9.81 m/s² downward. This concept is crucial for determining the height of the tabletop.

Projectile Motion

Projectile motion describes the motion of an object that is launched into the air and is subject to gravitational acceleration. Although the book slides off horizontally, its vertical motion is independent of its horizontal motion. The horizontal speed and the time of flight can be used to calculate the vertical distance fallen, which corresponds to the height of the tabletop.