plzz help mee. easy physics problem i am just stuckk?

Question

You are standing at the top of a cli® that has
a stairstep con¯guration. There is a vertical
drop of 5 m at your feet, then a horizontal
shelf of 8 m; then another drop of 5 m to the
bottom of the canyon, which has a horizontal
°oor. You kick a 0:43 kg rock, giving it an
initial horizontal velocity that barely clears
the shelf below. The acceleration of gravity is
9:8 m=s2 : Consider air friction to be negligi-
ble.



How far from the bottom of the second cli®
¢x will the projectile land? Answer in units
of m.

Answer 1

The rock falls 5 m and moves 8 m horizontally. Solving this for hor. v (vx) will enable calculating the answer.
h = gt^2/2; t1 = sqrt(2h/g) = sqrt(10/9.8)
vx = x1/t1 = 8/t1
t2 = sqrt(2h/g) = sqrt(20/9.8)
x2 = vx * t2 from the top, or vx * t2 - 8 from the foot of the cliff (answer in m).
A shorter way is to note that the shelf and total drop heights have a ratio of 2:1. Since time, and hor. distance travelled, are proportional to sqrt(h), the hor. distance from the top for the total drop is sqrt(2) * the hor. distance for the shelf drop, or 8*sqrt(2) m, 8*sqrt(2) - 8 m from the foot. You don't need to know the value of g.
P.S. If you had a cat, would you name it °u®y or ¯garo?