A cat chases a mouse across a 1.3 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.
What was the cat’s speed when it slid off
the table? The acceleration of gravity is
9.81 m/s
2
.
Answer in units of m/s
2.5m/s
To find the cat's speed when it slid off the table, we can use the principle of conservation of energy. We can assume that initially, all of the cat's potential energy is converted into kinetic energy when it reaches the floor.
The potential energy of an object is given by the equation U = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
The kinetic energy of an object is given by the equation K = 0.5mv^2, where m is the mass and v is the velocity or speed.
Since the potential energy is converted into kinetic energy, we can set the initial potential energy equal to the final kinetic energy:
mgh = 0.5mv^2
Dividing both sides of the equation by m and canceling out the mass, we get:
gh = 0.5v^2
Now we can plug in the given values:
g = 9.81 m/s^2 (acceleration due to gravity)
h = 1.3 m (height of the table)
9.81 * 1.3 = 0.5v^2
12.7533 = 0.5v^2
To solve for v, we need to isolate v^2 by dividing both sides by 0.5:
12.7533 / 0.5 = v^2
25.5067 = v^2
To solve for v, we can take the square root of both sides:
v = √25.5067
v ≈ 5.05 m/s
Therefore, the cat's speed when it slid off the table is approximately 5.05 m/s.