Answer :
The baseball has a speed of 107.73 m/s given its kinetic energy of 122 J and mass of 0.145 kg. The force applied by the pitcher to achieve this kinetic energy over a distance of 1.1 meters is 110.9 N.
To calculate the speed of the baseball, we use the relationship between kinetic energy and velocity. The kinetic energy (KE) of an object is given by the equation KE = 1/2 mv2, where m is mass and v is velocity. Given the kinetic energy of 122 J and the mass of the baseball is 0.145 kg, we can rearrange the equation to solve for v:
v = \(\sqrt{(2 \* KE) / m}\)
= \(\sqrt{(2 \* 122 J) / 0.145 kg}\)
= \(\sqrt{1682.76/0.145}\)
= \(\sqrt{11605.9}\)
= 107.73 m/s
Now, to calculate the force applied by the pitcher, we can use the work-energy principle.
The work done by the force is equal to the change in kinetic energy, which is 122 J. Work is also calculated by the equation Work = force (F) × distance (d). Given a distance of 1.1 meters,
F = Work / d
= 122 J / 1.1 m
= 110.9 N
Therefore, the pitcher applied a force of 110.9 N to the baseball to give it the kinetic energy of 122 J.
