You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 36.761s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

Answer 1

if t is RISE time
and Vi is initial speed up

v = Vi - 9.81 t
at top v = 0
so
Vi = 9.81 * 36.761/2
(because it spends half the time going up)

Now I hope you know 45 degrees gives max range
New Vi = Vi sin 45
U = Vi cos 45
with new Vi find time to top same way 9.81 t = Vi
time in air = 2 t
d = u * 2 t