A book slides off a horizontal tabletop. As it leaves the table’s edge, the book has a horizontal velocity of magnitude ${\mathit{v}}_{\mathbf{0}}$. The book strikes the floor in time t. If the initial velocity of the book is doubled to $\mathbf{2}{\mathit{v}}_{\mathbf{0}}$, what happens to (a) the time the book is in the air, (b) the horizontal distance the book travels while it is in the air, and (c) the speed of the book just before it reaches the floor? In particular, does each of these quantities stay the same, double, or change in another way? Explain.

The given data can be listed below,

• The magnitude of horizontal velocity is, $v_0$.
• The velocity after time t is, $2v_0$.

The rate of change of an object's location with regard to a frame of reference is its velocity, which is a function of time. Velocity is a measurement of a thing's direction and speed of motion.

The total time it takes for the book to reach the floor is determined by the height from which it is thrown and the acceleration caused by gravity. If you double the book's initial horizontal velocity, it will take the same amount of time to reach the ground as it did before since the horizontal velocity is unaffected.

Thus, the initial velocity is in the x-direction, it has no effect on the acceleration in the y-direction, the time would remain constant.

The horizontal distance reached by a book in the air is determined by the book's starting horizontal velocity and the time it takes to travel in the air.

Because the horizontal distance covered by the book is dependent on the starting velocity of the book in horizontal position and the time it travels in air, doubling the initial velocity in horizontal direction while keeping time fixed doubles the horizontal distance travelled by the book.

Thus, the horizontal distance would double if the initial velocity doubles and it travels twice as fast with double velocity.

The rate of change of an object's location with regard to a reference frame is its velocity, which is a function of time. Velocity is a measurement of a thing's direction and speed of motion.

Thus, the speed of book increase because the x-component is now twice as great in magnitude, the book's pace will shift.