Two inclined frictionless tracks, one gradual and the other steep meet at A, from where two stones are allowed to slide down from rest, one on each track. Will the stones reach the bottom at the same time? Will they reach there with the same speed? Given `theta_(1)=30^(@),theta_(2)=60^(@),h=10m`. What are the speeds and time taken by the two stones?

Explanation

(a) Let x and y represent two stones.
`v_(x)=v_(y)=sqrt(2gh)=sqrt(2xx10xx10)=10sqrt(2)ms^(-1)`
(b) `a_(x)=gsintheta_(1)=10xxsin30^(@)=5ms^(-1)`
`t_(x)=v//a_(x)=(10sqrt(2))/(5)=2sqrt(2)s`
`a_(x)^(1)=gsintheta_(2)=(10sqrt(3))/(2)=5sqrt(3)ms^(-1)`
`therefore t_(y)=(v)/(a_(y))=(10sqrt(2))/(5sqrt(3))=2sqrt((2)/(3))s`
Clearly `t_(y)ltt_(x)`, hence y reaches C earlier than x reaching B.