An autographed baseball rolls off of a 0.67 m
high desk and strikes the floor 0.37 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 falling 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 hits the floor.
Let's follow the steps to find the answer:
Step 1: Find the potential energy (PE) of the ball initially on the desk.
PE = mgh
where m is the mass of the baseball (which is not given), g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the desk (0.67 m).
Step 2: Find the final kinetic energy (KE) of the ball just before it hits the floor.
KE = 1/2 mv^2
where m is the mass of the baseball (which is not given), and v is the velocity of the ball just before hitting the floor.
Step 3: Set the initial potential energy equal to the final kinetic energy to find v.
mgh = 1/2 mv^2
m cancels out.
Step 4: Solve for v.
gh = 1/2 v^2
v^2 = 2gh
v = sqrt(2gh)
Step 5: Plug in the values and calculate.
v = sqrt(2 * 9.81 m/s^2 * 0.67 m)
Calculating this expression gives us:
v ≈ 3.40 m/s
Therefore, the speed at which the autographed baseball was rolling on the desk before falling off is approximately 3.40 m/s.