A bullet of mass M is fired with a velocity `50m//s` at an angle with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass 3M suspended by a massless string of length `10//3` metres and gets embeded in the bob. After the collision, the string moves through an angle of `120^@`. Find
(i) the angle `theta`,
(ii) the vertical and horizontal coordinates of the initial position of the bob with respect to the point of firing of the bullet. Take `g=10 m//s^2`

Answer

(i) `37^(@)` (ii) `(120, 45)`

Explanation

(i) `((u cos theta)/(4))^(2) = 2g ((3R)/(2))`
`rArr cos theta = 4//5 rArr theta = 37^(@)`
(ii) `x = (R )/(2) = (v^(2) sin^(2) theta)/(2g) = 120m`
`y = H = (u^(2) sin^(2) theta)/(2g) = 45m`