(Solved): Let v(t) and w(t) be the horizontal and vertical components, respectively, of the velocity of a batt ...

Let

and

be the horizontal and vertical components, respectively, of the velocity of a batted (or thrown) baseball. In the absence of air resistance,

and

satisfy the equations:

a. Show that

where

is the initial speed of the ball and

is its initial angle of elevation. b. Let

and

be the horizontal and vertical coordinates, respectively, of the ball at time

. If

and

, find

and

at any time

. c. Suppose the outfield wall is at a distance

and has height

. Find a relation between

and

that must be satisfied if the ball is to clear the wall. d. Suppose that

and

. Using the relation in part (c), find the range of values of A that correspond to an initial velocity of

.