Tom the cat is chasing Jerry the mouse across a table surface 2.4 m off the floor. Jerry steps out of the way at the last second, and Tom slides off the edge of the table at a speed of 2 m/s.What speed will Tom have just before he hits?
Vf^2 = Vo^2 + 2g*d,
Vf^2 = 0 + 19.6*2.4 = 47.04,
Vrf = 6.86m/s.
To find the speed at which Tom will hit the ground, we can use the principle of conservation of energy.
First, let's determine the potential energy Tom has just before sliding off the edge of the table. The potential energy is given by the formula:
Potential Energy = mass * gravity * height
Since we are only interested in the speed, we can ignore the mass of Tom. So the potential energy just before sliding off the table is:
Potential Energy = gravity * height
Where gravity is the acceleration due to gravity (approximately 9.8 m/s^2) and height is the distance from the table surface to the ground (2.4 m).
Potential Energy = 9.8 m/s^2 * 2.4 m
Potential Energy = 23.52 J
Now, let's find the kinetic energy just before Tom hits the ground. The kinetic energy is given by the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Again, we can ignore Tom's mass and calculate the kinetic energy as:
Kinetic Energy = (1/2) * velocity^2
We know that the potential energy just before sliding off the table will be converted into kinetic energy just before hitting the ground, so:
Potential Energy = Kinetic Energy
9.8 m/s^2 * 2.4 m = (1/2) * velocity^2
23.52 J = (1/2) * velocity^2
Solving for velocity:
velocity^2 = (2 * 23.52 J) / 1
velocity^2 = 47.04 J
velocity = √47.04 J
Therefore, the speed at which Tom will hit the ground is approximately 6.86 m/s.
To determine the speed at which Tom will hit the floor, we can use the principle of conservation of energy. At the edge of the table, Tom will possess only potential energy, which will be converted to kinetic energy as he falls.
First, let's calculate the potential energy (PE) of Tom at the edge of the table. The potential energy is given by the formula:
PE = m * g * h
Where:
m = mass of Tom
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height of the table (2.4 m)
Next, we need to calculate Tom's mass. Unfortunately, the question does not provide any information about Tom's mass, so we won't be able to calculate the exact value. However, we can still provide the formula and let you fill in the missing value.
The final formula to calculate the potential energy will be:
PE = m * 9.8 * 2.4
Once you obtain the potential energy value (PE), you can equate it to the kinetic energy (KE) at the moment just before Tom hits the floor, which is given by:
KE = 0.5 * m * v²
Where:
v = velocity of Tom just before hitting the floor
Now, let's plug in the values and solve for velocity (v):
PE = KE
m * 9.8 * 2.4 = 0.5 * m * v²
Simplifying the equation:
23.52 = 0.5 * v²
Divide both sides by 0.5:
v² = 23.52 / 0.5
v² = 47.04
Taking the square root of both sides:
v = √47.04
Therefore, the speed at which Tom will hit the floor is approximately 6.86 m/s.