On Tuesday, Kyle Schwarber hit a home run for the Cube, which landed on top of Wrigley Field's right-field video hoard and helped the Cubs win the National League Division Series against the St. Louis Cardinals. When hit, the ball had a speed of 165 feet per second heading 35^o above the horizontal.

a. Calculate the vertical and horizontal components of the ball's velocity, and v_y, and v_x, off the bat. This is equivalent finding the sides of the triangle below.

b. The height of the ball above the ground t seconds after it was hit is approximated by S_y (t) = v_y t - 16t². Insert the value of v_y you found in part (a) to determine the time at which the hall "turns around", that is, the time at which it stops rising.

c. Determine the maximum height of the hall using the formula for s_y and your result from the previous part. Determine the time at which the ball would have hit the ground, if it were not interrupted by the sign or another obstruction.

d. The horizontal distance of the ball from the batter is approximated by the function s_x (t) = v_x t - 10.87t² (10.87 is a constant chosen to approximate the effect of wind and drag). Use this function and your value for v_x from part (a) to determine how far the hall would have travelled away from the hatter before hitting the ground, if it were not interrupted by the sign or another obstruction.