A cat chases a mouse across a 1.7 m high

table. The mouse steps out of the way, and
the cat slides off the table and strikes the floor
2.1 m from the edge of the table.
The acceleration of gravity is 9.81 m/s2 .
What was the cat’s speed when it slid off
the table?
Answer in units of m/s.

To find the cat's speed when it slid off the table, we can use the principles of kinematics.

Step 1: Identify the known values
- Initial vertical position (y0) = 1.7 m (height of the table)
- Vertical displacement (Δy) = -1.7 m (since the cat comes down from the table)
- Horizontal displacement (Δx) = 2.1 m (distance from the edge of the table to the point where the cat strikes the floor)
- Acceleration due to gravity (g) = 9.81 m/s^2

Step 2: Find the time it takes for the cat to fall
We can use the kinematic equation for vertical motion: Δy = (1/2) * g * t^2
Substituting the known values and solving for t, we get:
-1.7 = (1/2) * 9.81 * t^2
Simplifying the equation, we get t^2 = (-1.7 * 2) / 9.81
Taking the square root of both sides, we find t = √((-1.7 * 2) / 9.81)

Step 3: Find the cat's initial horizontal velocity
To find the initial horizontal velocity, we can use the formula: v = Δx / t
Substituting the known values, we have:
v = 2.1 / (√((-1.7 * 2) / 9.81))

Step 4: Calculate the cat's speed
The cat's speed when it slid off the table is equal to its initial horizontal velocity. Therefore, the cat's speed is:
Speed = v = 2.1 / (√((-1.7 * 2) / 9.81))

Calculating this expression will give you the answer in units of m/s.

How long did it take for the mouse to fall 1.7m?

speed=horizontaldistance/timefalling

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