A cat chases a mouse across a 1.7 m high
table. The mouse steps out of the way, and
the cat slides off the table and strikes the floor
2.8 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 speed of the cat when it slid off the table, we can use the principle of conservation of energy.
First, let's calculate the potential energy the cat had at the edge of the table:
Potential energy (mgh) = mass (m) × acceleration due to gravity (g) × height (h)
Substituting the given values:
Potential energy (mgh) = m × 9.81 m/s^2 × 1.7 m
Next, let's consider the kinetic energy the cat had when it hit the floor. Since the cat is sliding, there is no vertical velocity component, so we only need to consider the horizontal velocity. We can use the equation for horizontal projectile motion to find the horizontal velocity:
Horizontal displacement (x) = horizontal velocity (v) × time (t)
Given that the cat struck the floor 2.8 m from the edge of the table, we know that the horizontal displacement (x) is 2.8 m.
Now, we need to find the time (t) it took for the cat to reach the floor. We can use the equation of motion for vertical motion:
Vertical displacement (y) = initial vertical velocity (0) × time (t) + (1/2) × acceleration due to gravity (g) × time (t)^2
Since the cat was at rest vertically (hence, initial vertical velocity = 0), the equation simplifies to:
Vertical displacement (y) = (1/2) × acceleration due to gravity (g) × time (t)^2
Since the cat fell from the edge of the table, the vertical displacement (y) is the height of the table, which is 1.7 m.
Substituting the values:
1.7 m = (1/2) × 9.81 m/s^2 × t^2
Now, solve for time (t). Taking the square root of both sides and rearranging the equation:
t = √(2 × 1.7 m / 9.81 m/s^2)
Once we find the time (t), we can simply divide the horizontal displacement (x) by the time (t) to find the horizontal velocity (v).
v = x / t
Substituting the values:
v = 2.8 m / t
Now, you can calculate the cat's speed when it slid off the table by substituting the value of t into the equation.
Please note that without specific values for the mass of the cat, we can only determine the speed in terms of a constant factor.