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

Question

prove that if a body is thrown vertically upwards, the time of
ascent is equal to the time of decent

Anmol Kapur · Accepted Answer

Time of ascent be t seconds and the object be thrown with an initial velocity be u m/s.

$n n n^{n v n n n 2 n n} n - n n^{n u n n n 2 n n} n = n n - n 2 n g n h n n \Rightarrow n n^{n 0 n n n 2 n n} n - n n^{n u n n n 2 n n} n = n n - n 2 n g n h n n \Rightarrow n n^{n u n n n 2 n n} n = n 2 n g n h n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n ... n (n 1 n) n n$

$n n t n n = n n \frac{n}{n v n - n u n} n n \Rightarrow n t n n = n \frac{n}{n u n} n n n$

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.

$n n n^{n v n n n 2 n n} n - n n^{n u n n n 2 n n} n = n 2 n g n h n n \Rightarrow n n^{n v n n n 2 n n} n - n n^{n 0 n n n 2 n n} n = n 2 n g n h n n \Rightarrow n n^{n v n n n 2 n n} n = n 2 n g n h n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n ... n (n 2 n) n n$

From equation (1) and (2) we can see that u = v.

$n n t n n' n = n \frac{n}{n v n - n u n} n n n n n n n n = n \frac{n}{n v n} n n = n n \frac{n}{n u n} n n$

t' = t, that is, time of ascent is equal to time of descent.

20

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