An autographed baseball rolls off of a 0.85 m
high desk and strikes the floor 0.68 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/s2 .
Answer in units of m/s
To find the speed of the baseball when it fell off the desk, we can use the principle of conservation of mechanical energy. We can equate the potential energy of the baseball when it was on the desk to the kinetic energy of the baseball when it fell off.
The potential energy (PE) of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point. In this case, the reference point is the floor, so h is the height of the desk (0.85 m).
The kinetic energy (KE) of an object is given by the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
Since there is no change in the mass of the baseball, we can equate the potential energy on the desk to the kinetic energy when it fell off:
mgh = (1/2)mv^2
Canceling out the mass, we get:
gh = (1/2)v^2
Rearranging the equation to solve for v, we get:
v = sqrt(2gh)
Substituting the values given, with g = 9.81 m/s^2 and h = 0.85 m, we have:
v = sqrt(2 * 9.81 m/s^2 * 0.85 m)
Calculating this, we find:
v ≈ 4.014 m/s
Therefore, the baseball was rolling on the desk with a speed of approximately 4.014 m/s before it fell off.