An olympic long jumper question

[Purp1eM0nsta]

Homework Statement

Long jumping

Relevant Equations

https://ibb.co/5GHjb2c

Trying to answer this question I made and turn it into a slideshow presentation on how to solve it​

I need to make a presentation on "the physics of long jumping" and one part I am struggling with is showing how to answer this question, I am struggling because i forget the important knowledge easily, and looking back at notes I've made confuses me even more, if i could have someone help me by taking a look at how I originally solved it, and explaining how i did actually do it? I am so sorry i just have a lot of learning struggles and i was paired with one of the most off-hands do it yourself teachers ever, so this has NOT been a good year for me :(
An olympic long jumper, initially going at a speed of 9 meters per second jumps with a take-off angle of 25 degrees.
Find:
-The amount of time the jumper stays in the air
-The horizontal distance the long jumper went
My work that I don't understand anymore/cant figure out how to convert into a slideshow presentation: https://ibb.co/5GHjb2c
if you need more context I'd be more than willing to give you chat logs i had with another tutor online, please help!

[Mentor Note -- Image pasted from external link into the thread]

 

[berkeman]

Homework Statement:: Long jumping
Relevant Equations:: https://ibb.co/5GHjb2c

An olympic long jumper, initially going at a speed of 9 meters per second

Why do you show a different number for ##V_{ix}## in the image of your work?

 

[kuruman]

You say that the acceleration in the x-direction is zero and that is correct. However, the expression you have for x as a function of time does not reflect that observation and is incorrect.

 

[haruspex]

You say that the acceleration in the x-direction is zero and that is correct. However, the expression you have for x as a function of time does not reflect that observation and is incorrect.

It's a bit hard to read the handwritten algebra (@Purp1eM0nsta , images are for diagrams and textbook extracts; please type algebra into the posts), but it looks to me that the penultimate line finishes with ##\frac 12 a_xt^2##, and a squiggle in the final line could be a zero substituted for the ##a_x##.