Question

when a stone is projected, it's horizontal range is 24m and greatest height 6m. find it's velocity of projection?

Answer 1

v = Vi - g t
at top v = 0
so
Vi = 9.8 t
h = 0 + Vi t -4.9 t^2
6 = 0 + Vi t - 4.9 t^2
t is half the time in the air
6 = 9.8 t^2 - 4.9 t^2 = 4.9 t^2
so
t = sqrt (6/4.9) = sqrt (1.22) = 1.10 seconds upward
Vi = 9.8 (1.1) = 10.8 m/s initial velocity upward component

time in air = 2 t = 2.2 seconds
u (2.2 seconds) = 24
so u = 24/2.2 = 10.9 m/s horizontal speed
so
velocity = 10.9 i + 10.8 j
about 15 m/s at about 45 deg