An autographed baseball rolls off of a 0.63 m
high desk and strikes the floor 0.46 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.
To find the speed at which the baseball was rolling on the desk before it fell off, we can use the conservation of energy principle.
The initial potential energy (PE) of the baseball when it was on the desk is equal to the final kinetic energy (KE) when it struck the floor.
The potential energy formula is given by:
PE = mgh
Where:
m = mass
g = acceleration due to gravity (9.81 m/s²)
h = height (0.63 m)
The kinetic energy formula is given by:
KE = 0.5mv²
Where:
m = mass
v = velocity
Since the mass of the baseball cancels out in both equations, we can equate the two expressions:
mgh = 0.5mv²
Simplifying the equation:
gh = 0.5v²
Now we can solve for v:
v² = 2gh
v = sqrt(2gh)
Substituting the values:
g = 9.81 m/s²
h = 0.63 m
v = sqrt(2 * 9.81 * 0.63)
Calculating the value:
v ≈ 3.95 m/s
Therefore, the baseball was rolling on the desk at a speed of approximately 3.95 m/s before it fell off.