A particle (m = 2 kg) slides down a smooth track AOC starting from rest at point A (height = 5m). After reaching point C (height =1m), the particle continues to move freely in air as a projectile. The particle velocity at point C is at angle `60^(@)` with the horizontal. The maximum height attained by particle after leaving point C is _____(in m). [figure drawn is schematic and hot to scale : take `=ms^(-2)`]

Answer

3

Explanation

At point C speed of particle is u
`:. 1/2 mv^2 = mg h " " implies 1/2 xx 2 xx u^2 = 2 xx 10 xx (5- 1) " " implies u^2 = 80`
`:. h_("max") = (u^2 sin^2 60^@)/(2 g) = (80 xx 3/4)/(20) = 3 m`.