A marble, rolling with speed 20 cm / s, rolls off the edge of a table that is 80 cm high. (a)

step 1 In this problem, first we have to determine the time required for the marble to reach the floor.

A marble, rolling with speed 20 cm / s, rolls off the edge...

A marble, rolling with speed $20 \mathrm{~cm} / \mathrm{s}$, rolls off the edge of a table that is $80 \mathrm{~cm}$ high. (a) How long does it take to drop to the floor? (b) How far, horizontally, from the table edge does the marble strike the floor?

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Key Concepts

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is subject only to the acceleration due to gravity. In this type of motion, the object's velocity can be decomposed into independent horizontal and vertical components, which allows the analysis of each direction separately.

Free Fall

Free fall is the motion of an object where gravity is the only force acting upon it. In the vertical direction, the object accelerates downward at a constant rate (approximately 9.8 m/s², or appropriately converted units), which is used to determine the time it takes to fall from a specific height.

Independence of Horizontal and Vertical Components

In projectile motion, the horizontal and vertical components of motion are independent. This means that the horizontal velocity does not affect the time taken to fall vertically, and the vertical acceleration due to gravity does not affect the horizontal distance covered, assuming negligible air resistance.

Kinematic Equations

Kinematic equations are mathematical expressions that relate displacement, velocity, acceleration, and time under constant acceleration. These equations are essential for solving problems involving projectile motion, as they allow us to calculate the time to fall and the horizontal distance traveled separately.

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