Traiettoria rettilinea

Studiamo il caso di una traiettoria rettilinea con inizio nel punto A sull'asse y [math]\left(A>0\right)[/math] e fine nel punto B sull'asse x [math]\left(B\ge0\right)[/math].[br][br]Ricaviamo le equazioni del moto scomponendo l'accelerazione di gravità [math]-g[/math] secondo le componenti tangenziale e normale lungo la traiettoria (l'ascissa curvilinea è considerata positiva nella direzione [math]A\longrightarrow B[/math]). [br]Detto [math]\alpha[/math] l'angolo che individua la pendenza della traiettoria, considerando le similitudini tra i triangoli rettangoli formati rispettivamente da traiettoria/assi e vettori accelerazione, risulta:[br][br][math]g_{\tau}=g\cdot sen\left(180-\alpha\right)=g\cdot sen\left(\alpha\right)[/math].[br][br][img]data:image/png;base64,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[/img][br][br]L'accelerazione della componente normale, d'altro canto, è annullata dal vincolo dell'immobilità della traiettoria.[br][br]Possiamo così calcolare le componenti [math]g_x[/math] e [math]g_y[/math] dell'accelerazione a cui è sottoposta una massa puntiforme (rispettivamente positive e negative rispetto ai riferimenti scelti). Risulta:[br][br][math]g_x=g_{\tau}\cdot cos\left(180-\alpha\right)=-g_{\tau}\cdot cos\left(\alpha\right)=-g\cdot sen\left(\alpha\right)cos\left(\alpha\right)[/math][br][math]g_y=-g_{\tau}\cdot sen\left(180-\alpha\right)=-g\cdot sen^2\left(\alpha\right)[/math][br][br]Integrando e imponendo la condizione iniziale di velocità nulla nel punto A, si ottengono le equazioni delle componenti velocità:[br][br][math]v_x=-gt\cdot sen\left(\alpha\right)cos\left(\alpha\right)[/math][br][math]v_y=-gt\cdot sen^2\left(\alpha\right)[/math][br][br]Tenendo conto delle relazioni trovate, integrando e applicando nuovamente le condizioni iniziali su A, si hanno in definitiva le seguenti equazioni del moto:[br][br][math]x\left(t\right)=-\frac{1}{2}gt^2\cdot sen\left(\alpha\right)cos\left(\alpha\right)[/math][br][math]y\left(t\right)=A-\frac{1}{2}gt^2\cdot sen^2\left(\alpha\right)[/math][br][br]Il tempo totale di caduta del corpo, fino ad arrivare al punto B, è dato da:[br][math]t_f=\sqrt{\frac{2A}{g\cdot sen^2\left(\alpha\right)}}[/math].

Information: Traiettoria rettilinea