# 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

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by sumeetvrm40

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by sumeetvrm40

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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