prove that if a body is thrown vertically upward , the time of ascent is equal to the time of - Science - Gravitation

Question

prove that if a body is thrown vertically upward , the time of
ascent is equal to the time of descent

Panchali Dutta · Accepted Answer

Ascent: Time of ascent be t seconds and the object be thrown with an initial velocity be u m/s $v^{2} - u^{2} = - 2 g h \Rightarrow 0^{2} - u^{2} = - 2 g h \Rightarrow u^{2} = 2 g h (1)$ $t = \frac{v - u}{- g} \Rightarrow t = \frac{u}{g}$ Descent: Time of descent be t' seconds and the object final velocity be v m/s The distance covered will be the same as when the object is thrown upwards $v^{2} - u^{2} = 2 g h \Rightarrow v^{2} - 0^{2} = 2 g h \Rightarrow v^{2} = 2 g h (2)$ From equation (1) and (2) we can see that u = v $t' = \frac{v - u}{g} = \frac{v}{g} = \frac{u}{g}$ t' = t, that is, time of ascent is equal to time of descent

prove that if a body is thrown vertically upward , the time of ascent is equal to the time of descent.