A cat chases a mouse across a 1.1 m high
table. The mouse steps out of the way, and
the cat slides off the table and strikes the floor
2.2 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.
How long did it take it to fall?
1.1 = 4.9 t^2
Solve for t
How far did it for at constant horizontal speed u?
2.2 = u t
u = 2.2/t , same t
4.64
To find the cat's speed when it slid off the table, we can use the principle of conservation of energy.
Step 1: Calculate the gravitational potential energy of the cat when it was on the table.
The potential energy formula is given by PE = m * g * h, where m is the mass of the cat, g is the acceleration due to gravity, and h is the height of the table.
Given: h = 1.1 m, g = 9.81 m/s^2.
Let's assume the mass of the cat is m.
PE = m * g * h
Step 2: Calculate the cat's kinetic energy just before it hit the floor.
Since the cat slid off the table, its potential energy is converted into kinetic energy. The kinetic energy formula is given by KE = 0.5 * m * v^2, where v is the speed of the cat just before it hit the floor.
Given: The cat's potential energy is converted entirely into kinetic energy when it reaches the floor.
PE (on the table) = KE (just before hitting the floor)
m * g * h = 0.5 * m * v^2
Step 3: Solve for v.
Let's solve for v using the equation from the previous step.
v^2 = (2 * g * h)
v = sqrt(2 * g * h)
Given: g = 9.81 m/s^2 and h = 1.1 m.
v = sqrt(2 * 9.81 * 1.1)
v ≈ sqrt(21.582)
v ≈ 4.64 m/s
Therefore, the cat's speed when it slid off the table was approximately 4.64 m/s.
To find the cat's speed when it slid off the table, we can use the principles of kinematics and the law of conservation of mechanical energy. Here's how you can find the answer:
1. First, we need to determine the height from which the cat slides off the table. We know that the height of the table is 1.1 m, but we need to consider the additional height the cat gained while sliding. Since the cat slides off the table and strikes the floor 2.2 m from the edge of the table, we can use the concept of a right-angled triangle to find the height. The horizontal distance travelled by the cat is the base of the triangle (2.2 m), and the height is the vertical distance from the base to the table (1.1 m). Using the Pythagorean theorem, the additional height can be calculated as follows:
Additional height = sqrt((horizontal distance)^2 - (table height)^2)
= sqrt((2.2 m)^2 - (1.1 m)^2)
2. Calculate the additional height using the equation:
Additional height = sqrt((2.2 m)^2 - (1.1 m)^2)
= sqrt(4.84 m^2 - 1.21 m^2)
= sqrt(3.63 m^2)
= 1.905 m (rounded to three decimal places)
3. Now that we know the total height from which the cat slides off, we can find the cat's speed using the equation for the conservation of mechanical energy. At the top of the table, the cat has only potential energy, which is then converted to kinetic energy as it slides down. The equation is given as:
Potential Energy (PE) = Kinetic Energy (KE)
mgh = (1/2)mv^2
where m is the mass of the cat, g is the acceleration due to gravity (9.81 m/s^2), h is the total height from which the cat slides, and v is the cat's speed.
4. Rearranging the equation to solve for v:
v = sqrt((2gh)/m)
5. Since we don't have information about the mass of the cat, we can assume that its mass cancels out and doesn't affect the final answer. Hence, we can calculate v using:
v = sqrt(2gh)
= sqrt(2 * 9.81 m/s^2 * 1.905 m)
= sqrt(37.725 m^2/s^2)
= 6.142 m/s (rounded to three decimal places)
Therefore, the cat's speed when it slid off the table was approximately 6.142 m/s.