The trajectory of a ball thrown from the outfielder to the catcher is given by:
ID: 2997785 • Letter: T
Question
The trajectory of a ball thrown from the outfielder to the catcher is given by:
where ? is the initial angle, v is the velocity, x is the distance, h is the height at which the ball leaves the outfielders hand and y is the height of the catchers glove. Use the bisection method with suitable initial guesses to determine ?, if v=40m/s, h=1.8m, x=100m, and y=1m.
The trajectory of a ball thrown from the outfielder to the catcher is given by: y = xtan (theta) - g/2v^2cos^2(theta) x^2 + h where ? is the initial angle, v is the velocity, x is the distance, h is the height at which the ball leaves the outfielder½s hand and y is the height of the catcher½s glove. Use the bisection method with suitable initial guesses to determine ?, if v=40m/s, h=1.8m, x=100m, and y=1m.Explanation / Answer
clear all
clc
v=40;
h=1.8;
x=100;
y=1;
g=9.81;
format long
f = inline('x*tan(t)-g/(2*v^2*cos(t)^2)*x^2+h');
eps_abs = 1e-5;
eps_step = 1e-5;
a = 0.0;
b = 90;
while (b - a >= eps_step || ( abs( f(g,h,a,v,x) ) >= eps_abs && abs( f(g,h,b,v,x) ) >= eps_abs ) )
c = (a + b)/2;
if ( f(g,h,c,v,x) == 0 )
break;
elseif ( f(g,h,a,v,x)*f(g,h,c,v,x) < 0 )
b = c;
else
a = c;
end
end
[a b]
abs( f(g,h,a,v,x) )
abs( f(g,h,b,v,x) )
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