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Question Number 160844 by Tawa11 last updated on 07/Dec/21

Answered by mr W last updated on 08/Dec/21

Commented by mr W last updated on 08/Dec/21

$$trackofmonkey:$$$$x_m=b$$$$y_m=h-\frac{{gt}^2}{2}$$$$trackofbullet:$$$$x_b=u\cos \theta t$$$$y_b=u\sin \theta t-\frac{{gt}^2}{2}$$$$with\tan \theta =\frac{h}{b}$$$$ifthereexiststatwhichbothtracks$$$$lieonthesameposition,thenit$$$$meansthatthebullethitsthemonkey.$$$$x_m=x_b\Rightarrow u\cos \theta t=b...\left(i\right)$$$$y_m=y_b\Rightarrow u\sin \theta t-\frac{{gt}^2}{2}=h-\frac{{gt}^2}{2}...\left(ii\right)$$$$from\left(i\right):t=\frac{b}{u\cos \theta }$$$$from\left(ii\right):t=\frac{h}{u\sin \theta }=\frac{b\tan \theta }{u\sin \theta }=\frac{b}{u\cos \theta }$$$$thatmeansatt=\frac{b}{u\cos \theta },thebullet$$$$hitsthemonkey.$$

Commented by Tawa11 last updated on 13/Dec/21

$$\mathrm{Wow},\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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