Consider a professional dart player. He is throwing the dart to hit the bullseye zone. We are focusing on the accuracy of his throws in the vertical axis, do not concentrate on the position of the darts in the horizontal axis. Just consider the players and dart motion in the sagittal plane. - Lets define a perfect throw as he hits the center point of the bullseye zone. Plot the trajectory of the perfect throw. - Find the tolerance for the initial velocity of the dart to hit the bullseye zone (assume that the throw angle is constant, find the minimum and maximum values of the initial velocity to hit the bullseye zone to stay within the lower and upper limits of the zone-). Show your calculations and plot the trajectories. - Find the tolerance for the throwing angle of the dart to hit the bullseye zone (assume that the initial velocity is constant, find the minimum and maximum values of the throwing angle to hit the bullseye zone to stay within the lower and upper limits of the zone-). Show your calculations and plot the trajectories. - Find the tolerance for the releasing time of the dart to hit the bullseye zone. Show your calculations and plot the trajectories. Hint: You have to make some assumptions such as the height, arm length of the player, and his posture during the throw. You have to find the formal distance of the player to the dart board and height of the bullseye from ground.