Convert a velocity of 72 km `h^(1-)` into `ms^(-1)` with the help of dimensional analysis.

Explanation

`n_1 = 72 km h^(-1) `
` n_2 = ? `
` L_1 = 1km `
` L_2= 1m`
` T_1 = 1h`
` T_2 = 1s`
` n_2 = n_1 [L_1/L_2]^a [T_1/T_2]^b`
The dimensional formula for velocity is ` [LT^(-1) ]`
a = 1 b = 1
`n_2 = 72 [ (1km)/(1m) ] [ (1h)/(1s) ]^(-1)`
` = 72 [ (1000 m )/(1m) ]^1 [ (3600s)/(1s) ]^(-1) = 72 xx 1000 xx 1//3600 = 20 ms^(-1)`
` = 72 km h^(-1) = 20 ms^(-1)`