Let u(t) and w(t) be the horizontal and vertical components, respectively, of the velocity of a...

Let u(t) and w(t) be the horizontal and vertical components, respectively, of the velocity of a batted baseball:

??=−?? and ??=−?−?? ?? ??

where ? is the coefficient of air resistance and g is the acceleration of gravity.

Determine u(t) and w(t) assuming the following initial conditions: ?(0) = ? cos ? and ?(0) = ? sin ?,where V is the initial speed of the ball, and A is its initial angle of elevation.
Let x(t) and y(t) be the horizontal and vertical coordinates, respectively, of the ball at time t. If?(0) = 0 and ?(0) = h, find x(t) and y(t) at any time t.
Plotthetrajectoryoftheballfor?=1/5,V=125ft/s,h=3ft,A=0.5rad,andg=32ft/s2.
Suppose that the outfield wall is at a distance L and has height H. Assuming that ? = 1/5, h = 3, L =

300 ft, and H = 10 ft, find the minimum initial velocity V and the optimal angle of elevation A for which the ball will clear the wall.

Expert Solution

orchestra answered 1 year ago

3.5.4 ([Ber14, Ex. 3.6.14]). Let T : V → W and S : W → U...

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explain the tradeoff between horizontal and vertical velocity

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