An autographed baseball rolls off of a 0.62 m
high desk and strikes the floor 0.33 m away
from the desk.
How fast was it rolling on the desk before
it fell off? The acceleration of gravity is
9.81 m/s
2
.
Answer in units of m/s
To find the speed at which the autographed baseball was rolling on the desk before it fell off, we can use the principles of conservation of energy.
The potential energy of the baseball when it was on the desk is converted into kinetic energy when it reaches the floor. Therefore, we can equate the potential energy of the baseball on the desk to the kinetic energy of the baseball when it reaches the floor.
The potential energy (PE) of an object can be calculated using the equation: PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.
Let's assume the mass of the baseball is m and the height of the desk is h.
So, the potential energy on the desk is: PE = mgh (1)
The kinetic energy (KE) of an object can be calculated using the equation: KE = 0.5mv^2, where v is the velocity of the object.
The kinetic energy when the baseball reaches the floor is: KE = 0.5mv^2 (2)
Since energy is conserved, we can equate equation (1) and equation (2):
mgh = 0.5mv^2
The mass of the baseball (m) cancels out:
gh = 0.5v^2
Now, we can solve for the velocity (v):
v^2 = 2gh
v = √(2gh)
Plugging in the given values of g = 9.81 m/s^2 and h = 0.62 m:
v = √(2 * 9.81 * 0.62)
v ≈ 3.07 m/s
Therefore, the autographed baseball was rolling on the desk at a speed of approximately 3.07 m/s before it fell off.