A ball is rolling on a table and leaves the end side of the table with a velocity of 1.5 m/s. The table is 0.70 m high and the ball has a mass of 0.850 kg. What's the speed of the ball when it hits the ground?
What equation should I use?
V^2 = Vo^2 + 2g*h
Vo = 0 = Vertical component of initial
velocity.
g = 9.8 m/s^2
h = 0.70 m.
Solve for V in m/s.
Note: The mass of the ball does not
matter.
To determine the speed of the ball when it hits the ground, we can use the principle of conservation of energy. The initial kinetic energy of the ball when it leaves the table is equal to the gravitational potential energy it gains as it falls.
First, let's calculate the potential energy of the ball when it is on the table. The potential energy (PE) is given by the formula:
PE = m * g * h
Where:
m = mass of the ball (0.850 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height of the table (0.70 m)
PE = 0.850 kg * 9.8 m/s^2 * 0.70 m = 5.397 J (Joules)
Since the ball is at rest on the table, its initial kinetic energy (KEi) is zero.
The total mechanical energy (E) of the ball is the sum of its kinetic energy (KE) and potential energy (PE):
E = KE + PE
At the moment the ball leaves the table, all the initial kinetic energy (KEi) is converted into potential energy (PE), so we have:
E = KEf + PE
Where:
KEf = final kinetic energy of the ball
PE = potential energy of the ball
Since the mechanical energy is conserved, we can equate the initial and final mechanical energies:
KEi + PE = KEf + PE
Since KEi = 0:
PE = KEf + PE
Now, we can solve for KEf (the final kinetic energy of the ball):
KEf = PE - PE
KEf = 5.397 J - 0 J
KEf = 5.397 J
The final kinetic energy (KEf) is equal to the initial kinetic energy the ball had when it left the table.
The speed (v) of the ball can be calculated using the formula:
KEf = 1/2 * m * v^2
Where:
m = mass of the ball (0.850 kg)
v = speed of the ball
Now, let's rearrange the equation to solve for v:
v^2 = 2 * KEf / m
v^2 = 2 * 5.397 J / 0.850 kg
v^2 = 12.694
v = √12.694 m/s
Therefore, the speed of the ball when it hits the ground is approximately 3.567 m/s.