Problem 2 Let u(t) and w(t) be the horizontal and vertical components, respectively, of the velocity...

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Problem 2 Let u(t) and w(t) be the horizontal and vertical components, respectively, of the velocity of a batted baseball: du dt where y is the coefficient of air resistance and g is the acceleration of gravity. a. Determine u(t) and w(t) assuming the following initial conditions: u(0) = V cos A and w(0) = V sin A, where Vis the initial speed of the ball, and A is its initial angle of elevation. dw dt = -yu and = -g - yw 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. Plot the trajectory of the ball for y = 1/5, V = 125 ft/s, h = 3 ft, A=0.5 rad, and g = 32 ft/s². d. Suppose that the outfield wall is at a distance L and has height H. Assuming that y = 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. Problem 2 Let u(t) and w(t) be the horizontal and vertical components, respectively, of the velocity of a batted baseball: du dt where y is the coefficient of air resistance and g is the acceleration of gravity. a. Determine u(t) and w(t) assuming the following initial conditions: u(0) = V cos A and w(0) = V sin A, where Vis the initial speed of the ball, and A is its initial angle of elevation. dw dt = -yu and = -g - yw 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. Plot the trajectory of the ball for y = 1/5, V = 125 ft/s, h = 3 ft, A=0.5 rad, and g = 32 ft/s². d. Suppose that the outfield wall is at a distance L and has height H. Assuming that y = 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.