A cat chases a mouse across a 1.5 m high
table. The mouse steps out of the way, and
the cat slides off the table and strikes the floor
1.0 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 concept of conservation of energy. At the table, the cat has potential energy due to its height, and this energy is converted into kinetic energy as it slides off and falls towards the floor.
The potential energy of the cat on the table can be calculated as the product of its mass (m) and the gravitational acceleration (g) and the height (h) of the table:
Potential energy (PE) = m * g * h
Substituting the given values:
PE = m * 9.81 * 1.5
When the cat reaches the floor, this potential energy is converted to kinetic energy (KE), given by the equation:
KE = (1/2) * m * v^2
where v is the cat's speed.
Equating the potential energy to the kinetic energy:
PE = KE
m * 9.81 * 1.5 = (1/2) * m * v^2
Simplifying the equation:
14.715 * m = (1/2) * m * v^2
Dividing both sides of the equation by m:
14.715 = (1/2) * v^2
Multiplying both sides of the equation by 2:
29.43 = v^2
Taking the square root of both sides:
v ≈ √29.43
Calculating the square root:
v ≈ 5.42 m/s
Therefore, the cat's speed when it slid off the table was approximately 5.42 m/s.
To find the cat's speed when it slid off the table, we need to use the concept of conservation of energy.
First, let's determine the potential energy of the cat when it was on the table and the kinetic energy of the cat when it reached the edge of the table.
1. Potential Energy (PE):
The potential energy of an object at a certain height can be calculated using the formula: PE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height.
In this case, the height (h) is given as 1.5 m and the acceleration due to gravity (g) is 9.81 m/s^2. Since we don't know the mass of the cat, we can ignore the m term since it will cancel out in the final calculations. So, the potential energy of the cat on the table is PE = g * h.
2. Kinetic Energy (KE):
The kinetic energy of an object can be calculated using the formula: KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
In this case, we are trying to find the velocity of the cat when it slid off the table, so the kinetic energy at that moment would be KE = (1/2) * m * v^2.
According to the principle of conservation of energy, the potential energy lost by the cat as it falls must be converted into kinetic energy when it reaches the edge of the table. So, we can set up an equation:
PE = KE
g * h = (1/2) * m * v^2
Now, we can plug in the given values:
g = 9.81 m/s^2
h = 1.5 m
9.81 * 1.5 = (1/2) * m * v^2
Solving for v^2:
v^2 = (2 * 9.81 * 1.5) / m
Since the mass cancels out, we don't need to know the mass of the cat to find the value of v^2.
v^2 = 29.43
Taking the square root of both sides, we get:
v = √29.43 ≈ 5.43 m/s
Therefore, the cat's speed when it slid off the table is approximately 5.43 m/s.
since the horizontal distance is d = vt, we need to know how long it took to fall 1.5m.
s = 1/2 at^2 = 4.9 t^2 = 1.5
t = .55 sec
So, 1 = .55v
v = 1.82m/s