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Answer :
The baseball's speed, determined using the kinetic energy formula, is approximately 41.02 m/s. The force applied by the pitcher is about 110.91 N, calculated from the work-energy theorem.
The question involves finding the speed of the baseball and the force applied by the pitcher. We use the kinematic and work-energy principles from physics.
To find the speed of the baseball, given its kinetic energy (KE) and mass (m), we use the kinetic energy formula:
KE = (1/2)mv2
Given KE = 122 J and m = 0.145 kg, solving for v (speed) gives:
v = sqrt(2*KE/m)
= sqrt(2*122 J / 0.145 kg)
= sqrt(1682.758)
= approx. 41.02 m/s
To determine the force (F) applied by the pitcher over the distance (d) of 1.1 meters that resulted in the baseball's kinetic energy, we use the work-energy theorem:
W = Fd = KE
Solving for F gives:
F = KE/d
= 122 J / 1.1 m
= approx. 110.91 N
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