An autographed baseball rolls off of a 0.55 m high desk and strikes the floor 0.82 m away from the desk.
The acceleration of gravity is 9.81 m/s2 .
How fast was it rolling on the desk before it fell off?
Answer in units of m/s.
To find the speed at which the baseball was rolling on the desk before it fell off, we can use the principle of conservation of mechanical energy.
The initial potential energy of the baseball on the desk is equal to the final kinetic energy of the baseball just before it strikes the floor. Assuming no additional forces (like air resistance), we can equate the initial potential energy to the final kinetic energy.
The potential energy of an object is given by the formula: PE = m * g * h
Where m represents the mass of the object, g represents the acceleration due to gravity, and h represents the height.
The kinetic energy, on the other hand, is given by the formula: KE = (1/2) * m * v^2
Where v represents the velocity of the object.
Since the mass of the baseball cancels out from both equations, we can set the potential energy equal to the kinetic energy and solve for v:
m * g * h = (1/2) * m * v^2
We can cancel out the mass of the baseball:
g * h = (1/2) * v^2
Now we can solve for v by rearranging the equation:
v^2 = 2 * g * h
Finally, we can take the square root of both sides to find the velocity:
v = √(2 * g * h)
Plugging in the values given in the question:
g = 9.81 m/s^2
h = 0.55 m
v = √(2 * 9.81 * 0.55)
v ≈ 3.986 m/s
Therefore, the baseball was rolling on the desk at a speed of approximately 3.986 m/s before it fell off.