A cat chases a mouse across a 1.0 m high
table. The mouse steps out of the way, and
the cat slides off the table and strikes the floor
2.3 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.
fell one meter
y = 1 + 0 t - 4.9 t^2
y = 0 at ground
so
t^2 = 1/4.9 = 0.204
t = .452 seconds
2.3 meters = u (.452)
u = 2.3 / .452
To find the cat's speed when it slid off the table, we can use the principle of conservation of energy. Initially, the cat has potential energy due to its position on the table. When it slides off, this potential energy is converted into kinetic energy.
The potential energy of the cat can be calculated using the formula: potential energy = mass * gravity * height. As the mass of the cat is not given, we can assume it cancels out in the final equation.
The kinetic energy of the cat can be calculated using the formula: kinetic energy = 0.5 * mass * velocity^2.
Since energy is conserved, we can equate the potential energy on the table with the kinetic energy when the cat slides off.
Potential energy on the table = kinetic energy when the cat slides off.
mass * gravity * height = 0.5 * mass * velocity^2.
We can rearrange this equation to solve for velocity:
velocity = sqrt((2 * gravity * height)).
Given that the acceleration of gravity (g) is 9.81 m/s^2 and the height (h) of the table is 1.0 m, we can substitute these values into the equation:
velocity = sqrt((2 * 9.81 m/s^2 * 1.0 m)).
Calculating this equation will give us the required speed of the cat when it slid off the table.
To find the cat's speed when it slid off the table, we can use the equations of motion.
First, we need to determine the time it took for the cat to fall from the table to the floor. We can use the equation:
d = v0*t + (1/2)a*t^2
Where:
d = distance (1.0 m)
v0 = initial velocity (unknown)
a = acceleration due to gravity (-9.81 m/s^2)
t = time
Since the cat did not have an initial vertical velocity (v0 = 0 m/s), the equation becomes:
d = (1/2)a*t^2
Rearranging the equation, we get:
t = sqrt((2*d)/a)
Substituting the given values:
d = 1.0 m
a = 9.81 m/s^2
t = sqrt((2*1.0)/(9.81))
t ≈ 0.451 s (rounded to three decimal places)
Next, we can calculate the horizontal distance traveled by the cat when it slid off the table. We can use the equation:
d = v*t
Where:
d = distance (2.3 m)
v = velocity (unknown)
t = time (0.451 s)
Rearranging the equation, we get:
v = d/t
Substituting the given values:
d = 2.3 m
t = 0.451 s
v = 2.3 / 0.451
v ≈ 5.1 m/s (rounded to one decimal place)
Therefore, the cat's speed when it slid off the table was approximately 5.1 m/s.