Calvin tests out his new slingshot by firing rocks at a pumpkin that he hangs from a tree branch, as shown. When the rocks hit the pumpkin, the pumpkin swings out and up, making a ballistic pendulum. Different-shaped rocks result in a different maximum angle θ that the rope makes with the vertical. However, each rock, regardless of its shape, has a mass m and is fired by Calvin with a horizontal velocity v0 from the same height. As Calvin experiments, he finds that different-shaped rocks produce three different results when they collide with the pumpkin:

- One type of rock collides with the pumpkin and remains embedded. The pumpkin swings out and up and makes an angle θembed.

- Another type of rock collides with the pumpkin and passes through it as it continues to travel. The pumpkin swings out and up and makes an angle θpass.

- Another type of rock bounces off the pumpkin and travels back towards Calvin. The pumpkin swings out and up and makes an angle θbounce.

(a) Rank the three angles θembed, θpass, and θbounce from greatest to least. You should label the greatest angle with "1", the next greatest with "2", and so on. You should use the same number for any two angles (or all three angles) that are the same.

(b) Justify your ranking in complete sentences.