Maximum altitude of a rocket in 2D motion and free body motion

[optoracko]

Homework Statement

A rocket is launched at an angle of 53 above the horizontal with an initial speed of 75 m/s. It moves for 25s along it's initial line of motion with an overall acceleration of 25 m/2². At this time its engines fail and the rocket proceeds to move as a freebody.

a) What is the rocket's maximum altitude?

Homework Equations

displacement = V₁time + (1/2)a(time)²
V² = V¹ + 2adisplacement

The Attempt at a Solution

I've googled this question after attempting it, and have seen several different methods from my own.

For part a, I'm interpreting it as the maximum vertical displacement. I set up a vector diagram, where the angle between the average velocity vector and horizontal velocity vector is 53. I use sin ratio to solve for the opposite, which is sinTHETA x hyp. This gives me 60m/s. I do the same process to find the vertical acceleration, which is 20.0 m/s². I plug them into the displacement equation, solve to get 7750m.

Now for the free body motion. Velocity will equal 0 when it gets to it's top. I use the second equation to rearrange for displacement. V2 is 0, V1 is -60², acceleration is -9.81. Essentially, displacement is a negative value. Meaning the max. altitude is still 7750m.

Makes sense to me, but I applied the same approach to a different question (identical) with diff. values. The answer was way off. (I did this to see if my approach was right).

What am I doing wrong?

 

[ƒ(x)]

What will be the rocket's velocity when it runs out of fuel?

V1 is -602

V1 isn't 60m/s because the rocket has been accelerating.