You\'re to come up with an estimate of a real kinematic quantity that you have n

Question

You're to come up with an estimate of a real kinematic quantity that you have no direct way of measuring: the acceleration a baseball undergoes while a baseball player is pitching it.

Make reasonable assumptions about physical quantities involved in pitching a baseball, then use them to calculate a rough estimate of the baseball's acceleration (and the elapsed time).

Since this is your first physical estimate, I'll tell you up front what you need to make assumptions about: choose reasonable values for the baseball's

•initial velocity v0

•final velocity v

•displacement x


For your response,

1.State and justify the assumed values for these three quantities, including symbols and units (SI only, please: no feet, yards, inches, etc.).

2.Apply what you know about kinematics to calculate an estimate of the baseball's acceleration a while the pitcher is pitching it. Show your work.

3.Check your estimated value for acceleration by using it to calculate an estimate of how long t the pitch lasts. Show your work.

4.Briefly discuss the estimated acceleration and time: do your results seem reasonable, or not? Explain.

Notes
Assumed values and calculated estimates should have 1 or at most 2 significant figures: these are not precise calculations, but rough estimates, and the SF's you use should reflect this. There is no single predetermined "right answer" you should be aiming for. The goal is to make a valid, realistic estimate.

Explanation / Answer

Say a person throws a 93mph fastball, starting from rest. If the pitcher extends his arm back, then begins the acceleration, and ends with his arm pointing forward, this is the displacement and perhaps it would be about, eh, 4ft? About 1.2m. So... 93mph* (1.609 kph/mph) = 149.6 km/h * (1000m/km) *(1h/3600s) = 41.56 m/s I know it says 1 or 2 sigfig...you started with 2 sigfig and the conversions from that point on are absolute; rounding too much during your conversions would give you a multi-sigfig original value if you reversed your conversion. v0=0m/s, vf=41.56 m/s, dx=1.2m vf^2=v0^2+2ax 41.56^2=0+2a*1.2 a= 719.7 m/s/s, or about 720 m/s/s Then, vf=v0+at; 41.56=0+720*t, t= 0.0577 or 57.7 ms That seems like a rather short period of time...a little more than half a tenth of a second. Considering human reaction time is what, a tenth or a couple tenths of a second? Either our assumptions are slightly off or not enough assumptions have been made. (e.g. does it make sense to view accelerating a baseball strictly as linear acceleration, neglecting any rotational components?)

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