a cat chases a mouse across a 1.6m high table. the mouse steps out of the way and the cat slides off the table and strikes the floor 2.0m from the edge of the table. what was the cat's speed when it slid off the table?

3.5

To find the cat's speed when it slid off the table, we can use the principle of conservation of energy. We'll consider two points: when the cat is on the table and when it reaches the floor.

First, let's calculate the potential energy of the cat when it was on the table. The potential energy formula is:

Potential Energy = mass * acceleration due to gravity * height

Given that the height of the table is 1.6m and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the potential energy as follows:

Potential Energy = mass * 9.8 m/s² * 1.6m

Next, let's determine the kinetic energy of the cat when it reached the floor. The kinetic energy formula is:

Kinetic Energy = (1/2) * mass * velocity²

We can rearrange this formula to solve for velocity:

Velocity = √(2 * Kinetic Energy / mass)

Here, Kinetic Energy is equal to the Potential Energy it had on the table.

Setting the potential energy equal to the kinetic energy, we can solve for the velocity:

mass * 9.8 m/s² * 1.6m = (1/2) * mass * velocity²

Simplifying the equation:

9.8 m/s² * 1.6m = (1/2) * velocity²

15.68 m²/s² = (1/2) * velocity²

31.36 m²/s² = velocity²

Taking the square root of both sides:

velocity = √31.36 m²/s²

Thus, the cat's speed when it slid off the table is approximately 5.606 m/s.