A ball of mass 500g is
kicked into the air at angle
of 45degree. It reaches a
height of 12m. What was
it's initial velocity?
First the vertical problem:
what is vertical component of velocity at launch ?
a = g = -9.81 m/s^2
v = Vinitial - 9.81 t
at top v = 0 so
t at top = Vi /9.81
h = 0 + Vi t - 4.9 t^2
at top h = 12
12 = Vi(Vi/9.81) - 4.9(Vi/9.81)^2
= Vi^2 /(2*9.81)
Vi^2 = 24*9.81
Vi = 15.3 m/s
Vi = initial speed *sin 45
so
initial speed = 15.3 / sin 45 = 21.6 m/s