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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'`
7 months ago

```							FOR VERTICALLY UPWARD MOTION:h=ut-1/2gt² _________(1)Also, v=u-gtAt height h, final velocity v=0;Therefore, u-gt=0u=gt(1)=h=gt²-1/2gt²h=gt²/2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ (A)FOR VERTICALLY DOWNWARD MOTION:v²=u²+2gh________(3)Also,v=u+gtIn this case, initial velocity at maximum height(h), I.e. u=0=>v=gtTherefore, v²=2ghg²t'²=2ghh=1/2gt’²_ _ _ _ _ _ _ _ _ _ _ _ _ _(B)(A)=(B)1/2gt²=1/2gt’²=>t=t'Therefore, h=0.5gt.t=>h=0.5gtt’
```
7 months 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’
```
7 months ago
```							 FOR VERTICALLY UPWARD MOTION:h=ut-1/2gt² _________(1)Also, v=u-gtAt height h, final velocity v=0;Therefore, u-gt=0u=gt(1)=h=gt²-1/2gt²h=gt²/2 _ _ _ _ _ _ _ _ _ _ _ _ _ _ (A)FOR VERTICALLY DOWNWARD MOTION:v²=u²+2gh________(3)Also,v=u+gtIn this case, initial velocity at maximum height(h), I.e. u=0=>v=gtTherefore, v²=2ghg²t'²=2ghh=1/2gt’²_ _ _ _ _ _ _ _ _ _ _ _ _ _(B)(A)=(B)1/2gt²=1/2gt’²=>t=t'
```
7 months ago
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