Computer Algebra Recipes

184 CHAPTER 4. NONLINEAR ODE MODELS
As much fun as she has had, Jennifer suddenly realizes that she had better
spend a little time hitting balls down at the local driving range before she goes
out with Heather and her friends. Otherwise, she might end up proving to be
an embarrassment to her sister. Now where did she put those golf clubs?
PROBLEMS:
Problem 4-29: The Bo®o brothers go gol¯ng
Syd and Benny Bo®o have taken an afternoon o® from their realty business
and gone gol¯ng at the Metropolis Country Club. After a good approach shot
on a level fairway, Benny Bo®o has placed his golf ball 100 m from the hole.
He selects a 9-iron and hits the ball perfectly, landing practically at the hole.
If both lift and drag are included and all other parameters of the text recipe
prevail, at what angle to the horizontal (in degrees) was the ball hit? How high
did the ball rise?
Problem 4-30: Syd Bo®o makes a hole in one
Syd and Benny Bo®o's golf match continues and they move onto the next hole,
a par 3. The tee-o® point is elevated 20 m above the hole, the ball having to
travel over an intervening lily pond. The horizontal distance from the tee-o®
position to the hole is 160 m. Syd miraculously scores a hole in one, which
means that drinks are on him at the clubhouse after the match. Assuming
that both lift and drag are included and all other parameters of the text recipe
prevail, at what angle did Syd's ball ascend in order for him to make the hole
in one? How high did the ball rise relative to the hole? If the green is circular
(radius 5 m) with the hole at its center, and the pond stretches up to the edge of
the green, would the ball have ended up in the pond if lift had been neglected?
Or would the ball have overshot the green?
Problem 4-31: Rocky Mountain high
At a Rocky Mountain golf resort, the elevation is such that the density of air is
½ =1:0 kg/m3and g =9:8 m/s2 .Howmuchfartherwouldtheballtravelthan
for the sea-level data given in the text recipe?
Problem 4-32: Horizontal drive
A golf ball that has been teed up 3 cm above the ground is hit badly and leaves
the tee horizontally. Including lift and drag and taking all other parameters as
in the text recipe, plot the trajectory of the ball and determine where it strikes
the ground, assuming that the fairway is level. How does the distance compare
to the situation in which there is no lift?
Problem 4-33: Vertical shot
As part of its testing routine, a golf ball manufacturing company tests the
performance of one of its golf balls by shooting it vertically into the air with
the same spin and other parameters as in the text recipe. If lift and drag are
included, where would the golf ball land?