A soccer ball is kicked by a soccer player from ground level with an initial launch angle of θ = 30.0°. It is aimed to land at the position of a second soccer player who is on the same team, and who is a distance d2 = 20.0 m away. It also needs to clear the height h = 1.80 m of a soccer player who belongs to the opposing team and who is a distance d1 = 8.00 m away from the first soccer player. Assume that the player positions are all along a straight line and that the players don't move during the motion of the ball.
a. Sketch this situation, including the coordinate system you are going to use and the trajectory of the soccer ball.
b. Write down the equations of motion (equations for x, y, vx , and v y ) for the soccer ball.
c. Write down the conditions imposed on the trajectory, assuming that the ball just clears the soccer player of the opposing team when it passes her.
d. Solve the equations of motion symbolically to obtain the launch speed of the ball v0 , the time when it clears the opposing player t1, and the time t2 when it arrives at the target player on the same team.
e. Use the numbers provided in the problem to obtain numerical values for these quantities.