Homework #2
Instructions. This is due on January 31 at the beginning of
class. It is worth 20 points. Late papers lose 3 points per day late. You must
work by yourself, but feel free to consult with me. Explain what you did and
why you did it! Your paper should have an introduction, a main body and a
conclusion. Start early, ask questions and do well.
Introduction. In the previous assignment,
we found that there are significant numerical differences in the two models for
the velocity of a falling object. The physical evidence is that for most
objects at most speeds, the velocity-squared model is more accurate. In this
assignment, we use that model to analyze two sports situations in which a ball
is moving horizontally. Use the general model (c is called the drag
coefficient):
dv/dt = - c v2
Problems. First,
briefly explain why gravity
is not included in the model. Then use the general model to solve the two
specific problems. In each case, precisely state the initial value problem,
solve it, integrate velocity to find position, and answer the question.
A pitcher throws a baseball (drag coefficient c
= 0.002 when velocity is given in ft/s) with initial velocity 90 mph. Determine
how long it takes to reach home plate 60 feet away and determine how fast it is
going at that point.
A tennis player serves a tennis ball (drag
coefficient c = 0.005 when velocity is given in ft/s) with initial
velocity 120 mph. Determine how long it takes to reach the net 39 feet away and
determine how fast it is going at that point. Determine how long it takes to
reach the service line 60 feet away and determine how fast it is going at that
point.
Both baseball and tennis commonly use radar guns to
measure the speeds of balls. Based on your calculations, does it matter much at
which point in the ball’s path the radar gun takes its measurement?