A rock is thrown with height, direction, and inital velocity provided

1. The problem statement, all variables and given/known data

A rock is thrown off a 100 m cliff at an angle of 38 degrees below horizontal with an initial velocity of 20.0 m/s.
a) What is the total time in flight?
b) What is the horizontal range?
c) What is the max height reached by the rock?

2. Relevant equations

x = x_0 + v_x t
y = y_0 + v_0y t – 1/2 g t^2

3. The attempt at a solution

The answers are
a) t = 3.43 s
b) R= 54.2 m
c) 100m, trick question.

I don’t get how the answers are made (I struggle with motion in two directions), but I’ve had them provided to me in class. I’m confused as to the process to get the answers. Above are the equations the instructor used in class, but I’m also confused as to why he used them. My book states only three kinematic equations, and those are:
v_f = v_0 + a t
Δx = v_0 t + 1/2 a t^2
v_f^2 = v_0^2 + 2 a Δx
and their vertical identicals.

Is it possible to get the answers using those three kinematic equations instead of the ones he used? Or can someone talk me through WHEN those two equations he used should be used? Like are they for projectile motion in two directions only or something?

Thanks in advance!

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