Question

The Green Monster, as shown below, is a wall 37 feet high in left field at Fenway Park in Boston. The wall is 310 feet from home plate down the third base line. If the batter hits the ball 4 feet above the ground, neglecting air resistance, determine the minimum speed that the bat must impart to the ball that is hit over the Green Monster. COVIDIE CVS. ELABOR The equations of motions for the baseball are x(t) = (u cos et and y(t) = y + (u sinetr as depicted in the diagram below. The ball's initial speed is u. The gravitational constant g is 9.8 m/sec. The height at which the ball is struck is yo. The coordinates depict the geometry with the origin at the home plate. The ball is struck at y = 4 ft. The top of the Green Monster, which is 310 feet from home plate, is noted as (310,37). (310,37) (0,4) (0,0) (310,0) In a well-documented MATLAB script hmwk8Q3.m, using vectorizing methods, plot the five baseball trajectories for the speeds u = 70, 80, 90, 100 and 110 mph. For all cases assume the baseball is hit at an angle 45 degrees with respect to the ground.

Answer 1

The matlab code is given below.

time = linspace(0,10);
speeds = [70,80,90,100,110];
x = zeros(100,5);
y = x;
xd = x;
yd = y;
ft2mtr = 0.3048;
mtr2ft = 1/ft2mtr;
mph2mps = 0.44704;
for i = 1:5
for j = 1:100
xd(j,i) = speeds(i)*mph2mps*0.707*time(j);
yd(j,i) = 4*ft2mtr + speeds(i)*mph2mps*0.707*time(j)-9.8*time(j)*time(j)/2;
end
end
x= xd*mtr2ft;
y = yd*mtr2ft;
plot(x(:,1),y(:,1))
hold on
plot(x(:,2),y(:,2))
hold on
plot(x(:,3),y(:,3))
hold on
plot(x(:,4),y(:,4))
hold on
plot(x(:,5),y(:,5))
xlim([0,310])
ylim([0,200])
yline(37)
legend('70','80','90','100','110')

The plot is given below.

50 100 150 200 250 300