A particle is projected vertically upwards from an elevated point. Magnitude of the velocity at height h above the starting point is found to be half of the magnitude of velocity at h height below the starting point. If maximum height reached by the particle above its initial point is mh/n then find (m-n).

Answer

2

Explanation

Let us be the magnitude of intial velocity which is directied upwards . Then as per given information , we can wirte the following :
`sqrt( mu^(2) - 2gh) = (1)/(2) sqrt( mu^(2) + 2gh)`
`rArr " " 4mu^(2) - 8 gh = mu^(2) + 2gh`
` mu^(2) = (10 gh)/(3)`
Maximum height attained by the body can be written as follows :
`H = (mu^(2))/(2g) = (5h)/(2)`
Comparing it with the given result we get m = 5 and n = 3 , hence value of m - n = 2 .
Hence answer is 2 .