a cat chases a mouse across a 0.55 m high table. The mouse steps out of the way, and the cat slides off the table and strikes the floor 2.7 m from the edge of the table. The acceleration of gravity is 9.81 m/s. what was the cats speed when it slid off the table?
To find the speed at which the cat slid off the table, we can use the principles of projectile motion and conservation of energy.
First, let's define some variables:
- The height of the table, h = 0.55 m
- The distance from the edge of the table to the point where the cat strikes the floor, x = 2.7 m
- The acceleration due to gravity, g = 9.81 m/s^2
When the cat slides off the table, it starts with zero initial vertical velocity (assuming it was at rest), and the only force acting on it is gravity. The vertical motion of the cat can be analyzed separately from its horizontal motion.
1. Vertical motion:
Using the equation for free fall motion:
h = (1/2) * g * t^2 (where t is the time of fall)
Rearranging the equation:
t = sqrt((2 * h) / g)
Plugging in the known values:
t = sqrt((2 * 0.55 m) / (9.81 m/s^2))
Calculating the time, t ≈ 0.327 seconds
2. Horizontal motion:
The horizontal distance traveled by the cat can be calculated using the equation of motion in the x-direction:
x = v * t (where v is the horizontal velocity and t is the time of motion)
Rearranging the equation gives:
v = x / t
Plugging in the values:
v = 2.7 m / 0.327 s
Calculating the horizontal velocity, v ≈ 8.26 m/s
Therefore, the cat's speed when it slid off the table is approximately 8.26 m/s.