A cat chases a mouse across a 1.1 m high

table. The mouse steps out of the way, and
the cat slides off the table and strikes the floor 1.2 m from the edge of the table. The acceleration of gravity is 9.81 m/s^2.What was the cat’s speed when it slid off the table?

Use

h=(1/2)gt²
to solve for t.
Horizontal velocity
=1.2 m / t

To find the cat's speed when it slid off the table, we can use the principles of projectile motion and conservation of energy.

Let's break down the problem into steps:

Step 1: Determine the height from which the cat slid off the table.
The cat slid off a table that is 1.1 m high. So, the height from which the cat slid off is also 1.1 m.

Step 2: Determine the time it takes for the cat to fall from the table.
First, we need to determine the time it takes for the cat to fall from the 1.1 m high table to the ground. We can use the equation for the distance fallen in free fall motion:

h = 0.5 * g * t^2

where:
h is the height (1.1 m)
g is the acceleration due to gravity (9.81 m/s^2)
t is the time

Rearranging the equation to solve for time (t), we have:

t = sqrt(2h/g)

Substituting the given values, we have:

t = sqrt(2 * 1.1 / 9.81) ≈ sqrt(0.224) ≈ 0.474 seconds

Step 3: Determine the horizontal distance traveled by the cat.
Given that the cat strikes the floor 1.2 m from the edge of the table, the horizontal distance traveled by the cat is 1.2 m.

Step 4: Determine the cat's speed when it slid off the table.
To find the cat's speed when it slid off the table, we can use the equation for horizontal distance traveled in projectile motion:

d = v * t

where:
d is the horizontal distance (1.2 m)
v is the horizontal velocity (the cat's speed)
t is the time (0.474 seconds)

Rearranging the equation to solve for velocity (v), we have:

v = d / t

Substituting the given values, we have:

v = 1.2 / 0.474 ≈ 2.532 m/s

Therefore, the cat's speed when it slid off the table was approximately 2.532 m/s.