Projectile motion thrown apple question

[Specter]

Homework Statement

A child sitting in a tree throws his apple core from where he is perched (4.0 m high) with a velocity of 5.0 m/s [35 degrees above the horizontal], and it hits the ground right next to his griend.

a) How long does it take for the apple core to hit the ground?
b) How far from the base of the tree will the apple core land?
c) What is the velocity of the apple core on impact?

Homework Equations

In the pictures below.

The Attempt at a Solution

I will include pictures of my documents because it is formatted better.

Part a)
1
2
Part b) How far from the base of the tree will the apple core land?
3

Part c) What is the velocity of the apple core on impact?
4

If typing it out would be better than the pictures I can do that. Just let me know.

Part c is where I am having the most trouble. I am not sure how to find the x component of the final velocity. I used 4.1 m/s in the solution but that is the x component of the initial velocity. If anyone could point out error, and help me figure this out that would be great!

Thanks :)

 

[TSny]

I think your work is correct. On page 4 you set up the calculation of the final y component of velocity correctly. But you state an answer of 5.052 m/s, which is incorrect. However, later when you apply the Pythagorean theorem, you use the correct value of 9.31 m/s.

Concerning your question about the final x component of velocity, you can answer that based on what you know about the x component of acceleration. What is the x component of the acceleration due to gravity?

On page 1 you say that your diagram is a FBD. But a free body diagram is a force diagram, not a velocity diagram.

Some homework helpers frown on solutions which are posted as pictures. This is because it is difficult to quote a particular part of your work.

But, overall your work looks good.

 

[Specter]

I think your work is correct. On page 4 you set up the calculation of the final y component of velocity correctly. But you state an answer of 5.052 m/s, which is incorrect. However, later when you apply the Pythagorean theorem, you use the correct value of 9.31 m/s.

Concerning your question about the final x component of velocity, you can answer that based on what you know about the x component of acceleration. What is the x component of the acceleration due to gravity?

On page 1 you say that your diagram is a FBD. But a free body diagram is a force diagram, not a velocity diagram.

Some homework helpers frown on solutions which are posted as pictures. This is because it is difficult to quote a particular part of your work.

But, overall your work looks good.

Alright, I'll try to fix the errors that you have mentioned. I will type everything out and post it here.

Do you know how I can format the text on this website like I did in the pictures I linked?

Thanks!

 

[TSny]

You do not need to retype your solution for this thread. But, next time it would be preferable to type out your work rather than post pictures of your work.

For formatting, there is a tool bar that you can use for superscripts, etc. If you click on the Σ symbol on the tool bar you will have access to various math symbols.

For diagrams, it is fine to upload a picture.

 

[Specter]

Concerning your question about the final x component of velocity, you can answer that based on what you know about the x component of acceleration. What is the x component of the acceleration due to gravity?

Would the x component of acceleration be 0?

 

[TSny]

Would the x component of acceleration be 0?

Yes. So, what does that imply about the x component of velocity?

 

[Specter]

Yes. So, what does that imply about the x component of velocity?

That it would also be zero. So I guess I just would leave it out of the solution, and what I have now is fine right?