Final answer:
To find the time it takes for the catcher to stop the baseball, calculate the acceleration using the given force and mass, then find the time it takes to change velocity from 37.1 m/s to 0 m/s using this acceleration. The calculated time is approximately 0.0423 seconds.
Step-by-step explanation:
Calculating the Time to Stop a Baseball
To calculate the time it takes for a baseball to come to a stop when a catcher feels a force of 193 N, you can use Newton's second law of motion, which relates force, mass, and acceleration (Force = mass × acceleration). Since acceleration is the change in velocity over time (a = Δv/Δt), we can rearrange the formula to solve for time (t).
Step 1: Calculate the acceleration using the given force and the mass of the baseball.
a = F/m where F = 193 N and m = 0.22 kg.
Step 2: Substitute the known values to find the acceleration. a = 193 N / 0.22 kg = 877.27 m/s².
Step 3: Use the calculated acceleration to find the time it takes for the baseball to stop
Since the final velocity (vf) of the baseball is 0 m/s (as it comes to a stop) and initial velocity (vi) is 37.1 m/s, we can calculate the time (t) as follows:
t = Δv/
a = (0 m/s - 37.1 m/s) / 877.27 m/s²
= 0.0423 s.