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 Quote by HelpMeh im sorry for the mess of equations but i have a final tomorrow night and my professor gives very little credit if we dont start from the basic equations of energy, kinematics, momentum, etc we arent allowed to make any shortcuts :( you get 80% credit for the problem as long as you have the correct equations setup and solved for the correct variable. and yes, energy is definitely not conserved when the bird was hit but we are asked to assume it is conserved.
I understand. In any case, the understanding which allows you to take shortcuts will also allow you to solve the question in whichever way you'd like to. And in this case, the basic energy equations are used in each of them, I just choose to sidestep kinematics.

I don't understand how energy can even be assumed to be conserved upon impact with the bird. Especially since the question states that the ball drops immediately after the impact, strongly suggesting an inelastic collision.

However, I do sympathize with your exam being tomorrow, and I understand that it cannot always be about the deep understanding, sometimes you just have to get sh*t done haha.

So in light of that, your answer to the first question is correct at 15.32 m/s (but the question asks you for velocity, you have just stated a speed. Don't forget to add that it's in the x-direction).

The second question asks you for the maximum height. How I would go about this is as follows: We know that the x-component of velocity does not play a role in the height. You've chosen to use a kinematic equation, and have ended up with a peculiar answer of 25.25 metres. At the maximum height, all of the initial kinetic energy from the y-component of velocity has been transferred to potential energy. Therefore you should have a simple
mgh = 1/2 m (Vinitial)^2, in which you could easily solve for h. Do you understand this? Make sure that you know that the initial velocity is only the y-component

As for the third question, which is apparently up for debate, I am going to assume it is an inelastic equation because I do not see a way to proceed in the case that energy is conserved. It asks you to find the speed right before it hits the ground, and these are the conclusions I will make before I try to calculate
-The ball collides with the bird when the y-component of velocity is 0
-The ball loses all x-component velocity upon impact (it falls straight down)
From these conclusions, I can only think one thing. This question could be simplified to, "What is the speed of a ball being dropped from the maximum height (from question 2) at the instant before it hits the ground."

Do you have any qualms with that interpretation of the question?