n this exercise, you\'re to come up with an estimate of a real kinematic quantit
ID: 1950351 • Letter: N
Question
n this exercise, 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.When you hire a contractor to work on a house project, the contractor makes reasonable assumptions about the labor and materials needed, then calculates an estimated cost based on those assumptions. You're going to to exactly the same thing: 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,
State and justify the assumed values for these three quantities, including symbols and units (SI only, please: no feet, yards, inches, etc.).
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.
Check your estimated value for acceleration by using it to calculate an estimate of how long t the pitch lasts. Show your work.
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.
Just as in real-life estimates given by contractors, there is no single predetermined "right answer" you should be aiming for. The goal is to make a valid, realistic estimate.
Explanation / Answer
The ball starts out not moving. When it leaves the pitcher's hand it is going 90mph - this is 40m/s. The ball has moved 1.5m. Do we have an equation that needs initial velocity v0 final velocity v displacement x and that gives us a? Look through your list and see. Vf^2 = Vo^2 + 2ad is what we want Vo = 0 Vf^2/2d = a (1600m^2/s^2)/3m = 500 m/s^2 Hmm. . . this is large, let's check our work The windup isn't really accelerating the ball, so lets say that the part of the pitch where the ball is speeding up is 0.1s Vf = Vo + at = 0 + 500M/S^2*0.1S = 50m/s This check of our work is encouraging, since we are "in the ballpark!" - ;) We are within 20% of our speed assumption, which is good for an estimate.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.