A cat chases a mouse across a 1.2 m high
table. The mouse steps out of the way, and
the cat slides off the table and strikes the floor
1.5 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?
Answer in units of m/s.
To find the cat's speed when it slid off the table, we can use the principle of conservation of energy. We'll equate the potential energy the cat had at the height of the table with the kinetic energy it had when it reached the floor.
1. First, let's find the potential energy (PE) of the cat when it was on the table. The potential energy can be calculated using the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
Height of the table (h) = 1.2 m
Acceleration due to gravity (g) = 9.81 m/s^2
Since the mass of the cat is not given, we can cancel it out in our calculations by dividing both sides of the equation by mass (m).
PE = mgh
PE/m = gh
2. Next, let's find the cat's initial kinetic energy (KE) when it slid off the table. We can use the equation: KE = (1/2)mv^2, where v is the cat's speed.
We need to make an assumption for the kinetic energy. Let's assume that the cat starts from rest, so the initial kinetic energy is zero.
KE = 0
3. Now, let's equate the potential energy (PE) and kinetic energy (KE):
PE/m = KE
gh = (1/2)v^2
4. Rearrange the equation to solve for v:
v^2 = 2gh
v = √(2gh)
5. Substitute the given values into the equation:
v = √(2 * 9.81 * 1.2)
6. Calculate the result:
v ≈ √(23.544) ≈ 4.851
Therefore, the cat's speed when it slid off the table was approximately 4.851 m/s.