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Question Number 196774 by BaliramKumar last updated on 31/Aug/23

$$$$A man standing on top of Burj Khalifa. If the height of Burj Khalifa including a man is 830 m, then what is the maximum distance up to which a man can see objects on Earth? (Earth's radius 6371 km)

Answered by Frix last updated on 31/Aug/23

$$h=.83\mathrm{km}$$$$r=6371\mathrm{km}$$$$$$$${(h+r)}^2=x^2+r^2$$$$x=\sqrt{h(h+2r)}\approx 102.84\mathrm{km}$$

Commented by BaliramKumar last updated on 31/Aug/23

Commented by BaliramKumar last updated on 31/Aug/23

$$\mathrm{Please}\mathrm{Sir},\mathrm{green}\mathrm{arc}\mathrm{distance}\mathrm{solution}$$

Commented by mahdipoor last updated on 31/Aug/23

$$cos\alpha =\frac{r}{h+r},arc=r\alpha$$

Commented by Frix last updated on 01/Sep/23

$$\mathrm{Yes}.$$

Commented by mr W last updated on 01/Sep/23

$$\alpha ={\cos }^{-1}\frac{6371}{6371+0.83}\approx 0$$$$\alpha \approx \tan \alpha$$$$arc=r\alpha \approx r\tan \alpha =x$$$$compare:$$$$arc=ra=102.833km$$$$x=r\tan \alpha =102.842km$$

Commented by BaliramKumar last updated on 01/Sep/23

$$\mathrm{thanks}\mathrm{sir}$$

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