A projectile fired at an angle of `45^(@)` travels a total distance R, called the range, which depends only on the initial speed v and the acceleration of gravity g. Using dimensional analysis, find how R depends on the speed and on g.

Answer

`R=Kv^(2)/g`

Explanation

`R prop v^(a)g^(b) rArr [L]=[LT^(-1)]^(a)[LT^(-2)]^(b)`
`rArr a+b=1, -a-2b=0`
`rArr a=2, b=-1 rArr R prop v^(2)/g`