# A stone is thtown at an angle thitha q to the horizontal reaches a maximum hieght h what will be the time of flight of stone

1
by sumeetvrm40

2014-04-11T08:47:09+05:30
First of all find the time in horizontal direction
for motion in horizonrtal direction
initial velocit,u=ucosx
acceleration,a=0
distance,S=x
time,t=t
so,by second law of motion
x=ut+1/2*a(t*t)
x=ucosx.t+0
t=x/ucosx
then,
for motion in vertical direction
initial velocity,u=usinx
acceleration,a=g
distance,S=y
time,t=t
similarly by second law of motion
y=ut+1/2*a*(t*t)
y=usinx.t+1/2*g(t*t)
putting value of t from above
y=usinx.(x/ucosx)+1/2*g*(x/ucosx*x/ucosx)
finally you'll get
y=utanx*x+g/2(u*u)*cos*cosx*(x*x)
and this is a equation of parabola

Mow the time of flight in air
means motion in vertical direction
therefore,In vertical direction
time,t=Total time /2
acceleration,a=-g
final velocity,v=0
initial velocity,u=usinx
then,
by first law of motion
v=u+at
0=usinx-g*T/2
Ultimatily,
Time of flight is,T=2usinx/g

hope you'll understand