A ball rolls of the top fi a strair way with horizonntal velocity of magnitude ` 1. 8 ms^(-1)`. The steps are ` 0.20 m` high and ` 0.02 m` wide , Which step will the ball it first ? ( g = 10 m//s^@)`.

Answer

fourth step

Explanation

`x = 0.2 m, nx = (1)/(2) "gt"^2, nx gt ut rArr n^2 x^2 gt u^2 t^2`
`rArr n^2 x^2 gt (u^2 2 nx)/(g)`
`rArr n gt (2 u^2)/(gx)`
`rArr n gt (2(1.8)^2)/(2 xx 0.2) rArr n gt 3.24`
and `(n - 1) x = (1)/(2) "gt"_1^2 rArr ut_1 gt (n - 1) x`
`rArr u^2 t_1^2 gt (n - 1)^2 x^2 rArr (u^2 2(n -1)x)/(g) gt (n - 1)^2 x^2`
`rArr (2 u^2)/(g x) gt n - 1 rArr n - 1 lt 3.24 rArr n lt 4.24`
Hence, ball will hit the fourth step first.
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