An autographed baseball rolls off of a 1.4 m high desk and strikes the floor 0.86m away from the desk. The acceleration of gravity is 9.81m/s squared. How fast was it rolling on the desk before it fell of? Answer in units of m/s.
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To find the initial speed at which the autographed baseball was rolling on the desk before it fell off, we can use the principle of conservation of energy.
The gravitational potential energy (PE) of the baseball at the top of the desk is converted into its kinetic energy (KE) when it rolls off and hits the floor.
The potential energy can be calculated using the equation:
PE = mgh
Where m represents the mass of the baseball, g is the acceleration due to gravity, and h is the height of the desk.
The kinetic energy is given by the equation:
KE = 1/2 mv^2
Where v represents the initial velocity or speed of the baseball rolling on the desk.
Since energy is conserved, we can set the potential energy equal to the kinetic energy:
mgh = 1/2 mv^2
Simplifying the equation by canceling out the mass (m) on both sides, we get:
gh = 1/2 v^2
Now, plugging in the known values:
g = 9.81 m/s^2 (acceleration due to gravity)
h = 1.4 m (height of the desk)
9.81 * 1.4 = 0.5 v^2
Rearranging the equation to solve for v:
v^2 = (2 * 9.81 * 1.4) / 0.5
v^2 = 27.3648
Taking the square root of both sides:
v = √27.3648
v ≈ 5.23 m/s
Therefore, the autographed baseball was rolling on the desk with an initial speed of approximately 5.23 m/s before it fell off.