Question

The magnitude of the velocity of a projectile when it is at its maximum height above ground level is 14 m/s. (a) What is the magnitude of the velocity of the projectile 1.2 s before it achieves its maximum height? (b) What is the magnitude of the velocity of the projectile 1.2 s after it achieves its maximum height? If we take x = 0 and y = 0 to be at the point of maximum height and positive x to be in the direction of the velocity there, what are the (c) x coordinate and (d) y coordinate of the projectile 1.2 s before it reaches its maximum height and the (e) x coordinate and (f) y coordinate

Answer 1

When the projectile is at its maximum height above ground, it's at the point
of changing from rising to falling.  At that exact point, its vertical speed is zero,
so the 14 m/s must be all horizontal velocity.  That's not going to change.

Since we need to consider changes in vertical speed now, we need to make
some assumption about where this is all happening, so that we know the
acceleration of gravity.  I'll assume that it's all happening on or near the Earth,
and the acceleration of gravity is 9.8 m/s².

I'm also going to neglect air resistance.

a). 1.2 sec before it reaches its maximum height, the projectile is rising
at a vertical speed of (1.2 x 9.8) = 11.76 m/s. 
The magnitude of its velocity is

the square root of (14² + 11.76²) = 18.28 m/s, directed about 40° above horizontal.

b).  1.2 sec after it reaches its maximum height, the projectile is falling
at a vertical speed of (1.2 x 9.8) = 11.76 m/s. 
The magnitude of its velocity is

the square root of (14² + 11.76²) = 18.28 m/s, directed about 40° below horizontal.

===========================

In 1.2 second before or after zero vertical speed, an object in free fall moves

         (1/2) (g) (t²) = (4.9) (1.2²) = 7.06 meters .

c). & d).
1.2 seconds before it reaches maximum height, the projectile is located at

           x = -14 m
           y = -7.06 m

e). & f).
1.2 seconds after it reaches maximum height, the projectile is located at

           x = +14 m
           y = -7.06 m .


I hope you recognize that 6 answers, plus a little bit of explanation,
all for 5 points, ain't too shabby.  You made out well.