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 1.4 m from the edge of the table. 2 The acceleration of gravity is 9.81 m/s .
What was the cat’s speed when it slid off the table?
Answer in units of m/s.
2.545
To find the cat's speed when it slid off the table, we can use the concept of kinematics and apply the laws of motion.
First, let's break down the information given:
Height of the table, h = 1.5 m
Distance from the edge of the table to the place where the cat strikes the floor, d = 1.4 m
Acceleration due to gravity, g = 9.81 m/s²
Now, let's define some variables:
Initial velocity of the cat on the table, u
Final velocity of the cat when it slides off the table, v
Time taken by the cat to fall, t
We can use the kinematic equation related to vertical motion:
h = ut + (1/2)gt²
Since the cat starts from rest on the table, the initial velocity u is 0. Therefore, the equation becomes:
h = (1/2)gt²
Now we can solve for t:
t² = (2h) / g
t² = (2 * 1.5) / 9.81
t² ≈ 0.3052
t ≈ √0.3052
t ≈ 0.5528 s
Now, we can calculate the cat's speed when it slid off the table using the horizontal motion. The horizontal distance d is covered in time t, and the initial velocity in the horizontal direction is also 0. Therefore, we can use the equation:
d = vt
Solving for v:
v = d / t
v = 1.4 / 0.5528
v ≈ 2.53 m/s
Therefore, the cat's speed when it slid off the table is approximately 2.53 m/s.