Question

A catapult is launching rocks at your village. It is hiding in a forest. All you can measure is that
the rock just passes over an 8 meter tall tree that is 73 meters from the village and that it takes 3
seconds for the rock to arrive from that moment.

How far is the catapult from the village?

Answer 1

No Idea if I am doing this right.
But so far what I done was

10.5Sin(67.6) = - gΔt
and got -9.71

Answer 2

u = horizontal speed = 73/3 = 24.3 m/s

falls 8 meters in 3 seconds
h = Hi + Vi t - 4.9 t^2
0 = 8 + 3 Vi - 9(4.9)
Vi = 12 m/s upward speed at tree top of 8 m

so let's find the top above that tree
v = Vi -9.81 t
0 = 12 - 9.81 t
t = 1.22 seconds rising above tree
so
h at top
h = 8 + 12(1.22) - 4.9 (1.22)^2
h = 15.3 meters high at top
so
falls to ground from 15.3 meters
How long to fall?
h = (1/2) g t^2
15.3 = 4.9 t^2
t = 1.77 seconds in the air falling
same time rising
so
total time in air = 3.54 seconds at horizontal speed of 24.3 m/s
so
answer is 3.54 * 24.3 = 86 meters