1. A basketball player is attempting a free throw and aims to get the ball falls through the center of the hoop, which is located a horizontal distance of 4.2 m down the court from the free throw line. The player releases the ball from their hand at a height of 2 m above the floor, and the hoop is located another 3 m above ground level. The initial launch speed of the ball is 7.6 m/s.

(a) Draw a simple diagram that illustrates the situation described above, clearly labelling all of the given measurements. (b) Start with the zero-drag projectile solution from class that gives the range as a function of launch angle, making sure to not forget the sign! Show that there are two possible launch angles for which the ball can pass through the center of the hoop: 40.5 and 62.9. Generate a plot of the two corresponding trajectories. (c) Show that the trajectory corresponding to the smaller launch angle is too shallow, in the sense that the basketball approaches the hoop at too sharp an angle to pass through. Here, you will need to use the fact that the ball diameter is 24cm and the hoop diameter is 46cm. (a) Draw a simple diagram that illustrates the situation described above, clearly labelling all of the given measurements. (b) Start with the zero-drag projectile solution from class that gives the range as a function of launch angle, making sure to not forget the sign! Show that there are two possible launch angles for which the ball can pass through the center of the hoop: 40.5 and 62.9. Generate a plot of the two corresponding trajectories. (c) Show that the trajectory corresponding to the smaller launch angle is too shallow, in the sense that the basketball approaches the hoop at too sharp an angle to pass through. Here, you will need to use the fact that the ball diameter is 24cm and the hoop diameter is 46cm