Grade 12th passMechanics

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

7 Years agoGrade 12th pass

3 Answers

prince sunjot dutt

7 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

7 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

7 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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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

3 Answers

prince sunjot dutt

JOSEPH KIMUTAI

abc

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