A cat chases a mouse across a 0.51 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/s2 .
What was the cat’s speed when it slid off
the table?
Answer in units of m/s.
First, calculate the time T that it takes to fall Y = 0.51 m. That time will not be affected by the initial horizontal velocity.
Since Y = (1/2) g T^2,
T = sqrt(2Y/g) = 0.323 s
The initial velocity can be computed from the horizontal distance X that the mouse travels while falling, since
X = V T .
Solve for V
To find the cat's speed when it slid off the table, we can use the equations of motion and the principle of conservation of energy.
First, let's find the time it takes for the cat to fall from the table to the floor. We can use the equation:
h = (1/2) * g * t^2
Where h is the height of the table (0.51 m), g is the acceleration due to gravity (9.81 m/s^2), and t is the time. Rearranging the equation, we get:
t^2 = (2 * h) / g
t^2 = (2 * 0.51) / 9.81
t^2 = 0.104
t ≈ 0.323 s (taking the square root)
Now that we have the time, we can use it to find the horizontal distance traveled by the cat before hitting the floor. We can use the equation:
d = v * t
Where d is the horizontal distance (1.5 m), v is the cat's speed, and t is the time (0.323 s). Rearranging the equation, we get:
v = d / t
v = 1.5 / 0.323
v ≈ 4.64 m/s
Therefore, the cat's speed when it slid off the table was approximately 4.64 m/s.