Final answer:
To calculate the force required to catch and stop a baseball, we use Newton's second law to determine the acceleration and then multiply by the mass of the baseball. The resulting force is approximately -200 N, indicating its direction is opposite to the ball's initial motion.
Step-by-step explanation:
The question involves calculating the force exerted on a baseball by a catcher to stop it. The baseball's mass is 0.15 kg, it's initially traveling at 40 m/s, and it is stopped within 0.03 s. To find the force, we use the formula derived from Newton's second law of motion, F = m × a, where m is the mass and a is acceleration. However, first we need to calculate the acceleration using the change in velocity (Δv) and the time it takes to change that velocity (Δt), with the formula a = Δv / Δt. The final velocity (vf) is 0 m/s since the ball is stopped, and the initial velocity (vi) is 40 m/s, so Δv = vf - vi = 0 m/s - 40 m/s = -40 m/s (the negative sign indicates a decrease in speed). Now, with Δt = 0.03 s, the acceleration is a = (-40 m/s) / 0.03 s = -1333.33 m/s². Finally, we calculate the force as F = m × a = 0.15 kg × -1333.33 m/s², yielding F ≈ -200 N. The negative sign indicates the force's direction is opposite to the ball's initial motion.