Is My Calculation of 81.48 Meters in Projectile Motion Correct?

[Kingyou123]

Homework Statement

Check for first upload

Homework Equations

I wrote them down in my attempt at a solution

The Attempt at a Solution

Second upload, 81.48 meters high seems really wrong to me...

 

[Student100]

As an aside, looking at your work is hard to follow. I think you could work on your organizational skills and hold off a bit more before plugging in numbers.

Your height at 95 meters downrange is incorrect, why don't we break this problem into segments. What are you trying to find initially to solve this problem?

 

[RUber]

Since the launch angle is 45 degrees, you can make use of the fact that vx = vy for the components of initial velocity.

 

[haruspex]

The formula you quote at the end of line 6 (d= etc.) is only valid when there is no net vertical displacement.
I heartily endorse Student100's advice to avoid plugging in numbers until the very end. Work the algebra entirely symbolically. Much easier to follow, to check for dimensional consistency, to spot algebraic mistakes...