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 the height of the tabletop above the floor.

Verified step by step guidance

1. Identify the known values: initial horizontal speed \( v_x = 1.10 \text{ m/s} \) and time \( t = 0.480 \text{ s} \).
2. Recognize that the vertical motion is independent of the horizontal motion. The book falls freely under gravity, so use the formula for vertical displacement: \( h = \frac{1}{2} g t^2 \), where \( g \) is the acceleration due to gravity \( 9.81 \text{ m/s}^2 \).
3. Substitute the known values into the formula: \( h = \frac{1}{2} \times 9.81 \text{ m/s}^2 \times (0.480 \text{ s})^2 \).
4. Calculate the expression inside the parentheses first: \( (0.480 \text{ s})^2 \).
5. Multiply the result by \( \frac{1}{2} \times 9.81 \text{ m/s}^2 \) to find the height \( h \).

Key Concepts

Kinematics in One Dimension

Kinematics is the study of motion without considering the forces that cause it. In this problem, we use the kinematic equations to determine the vertical motion of the book. The key equation is h = 0.5 * g * t^2, where h is the height, g is the acceleration due to gravity (9.81 m/s²), and t is the time (0.480 s).

Free Fall

Free fall describes the motion of an object under the influence of gravitational force only. In this scenario, the book falls freely after leaving the tabletop, meaning its vertical motion is solely affected by gravity. This allows us to use the kinematic equations for free-falling objects to find the height of the tabletop.

Independence of Motion

The principle of independence of motion states that horizontal and vertical motions are independent of each other. In this problem, the horizontal speed of the book (1.10 m/s) does not affect its vertical fall. Thus, we can separately analyze the vertical motion to find the height of the tabletop using the time it takes to hit the floor.