Let
v(t)
and
w(t)
be the horizontal and vertical components, respectively, of the velocity of a batted (or thrown) baseball. In the absence of air resistance,
v
and
w
satisfy the equations:
(dv)/(dt)=0,(dw)/(dt)=-g
a. Show that
v=ucosA,w=-gt usinA
where
u
is the initial speed of the ball and
A
is its initial angle of elevation. b. Let
x(t)
and
y(t)
be the horizontal and vertical coordinates, respectively, of the ball at time
t
. If
x(0)=0
and
y(0)=h
, find
x(t)
and
y(t)
at any time
t
. c. Suppose the outfield wall is at a distance
L
and has height
H
. Find a relation between
u
and
A
that must be satisfied if the ball is to clear the wall. d. Suppose that
L=350ft
and
H=10ft
. Using the relation in part (c), find the range of values of A that correspond to an initial velocity of
u=110f(t)/(s)
.