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A particle thrown vertically upwards takes t seconds to reach to a height h and t' seconds in the subsequent time to reach the ground again. Show that, h = 0.5gtt'

Saikat Das , 5 Years ago
Grade 12th pass
anser 3 Answers
prince sunjot dutt

Last Activity: 5 Years ago

FOR VERTICALLY UPWARD MOTION:
h=ut-1/2gt² _________(1)
Also, v=u-gt
At height h, final velocity v=0;
Therefore, u-gt=0
u=gt
(1)=
h=gt²-1/2gt²
h=gt²/2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ (A)
FOR VERTICALLY DOWNWARD MOTION:
v²=u²+2gh________(3)
Also,v=u+gt
In this case, initial velocity at maximum height(h), I.e. u=0
=>v=gt
Therefore, v²=2gh
g²t'²=2gh
h=1/2gt’²_ _ _ _ _ _ _ _ _ _ _ _ _ _(B)
(A)=(B)
1/2gt²=1/2gt’²
=>t=t'
Therefore, h=0.5gt.t
=>h=0.5gtt’

JOSEPH KIMUTAI

Last Activity: 5 Years ago

s=ut+0.5gt^2,  when s=0,u=0,therefore,s=0.5gt^2,    t^2=tt,  but t=t’,hence tt=tt’ replacing s with h, we get h=0.5gtt’

abc

Last Activity: 5 Years ago

 
FOR VERTICALLY UPWARD MOTION:
h=ut-1/2gt² _________(1)
Also, v=u-gt
At height h, final velocity v=0;
Therefore, u-gt=0
u=gt
(1)=
h=gt²-1/2gt²
h=gt²/2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ (A)
FOR VERTICALLY DOWNWARD MOTION:
v²=u²+2gh________(3)
Also,v=u+gt
In this case, initial velocity at maximum height(h), I.e. u=0
=>v=gt
Therefore, v²=2gh
g²t'²=2gh
h=1/2gt’²_ _ _ _ _ _ _ _ _ _ _ _ _ _(B)
(A)=(B)
1/2gt²=1/2gt’²
=>t=t'

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