A `24-kg` projectile is fired at an angle of `53^(@)` above the horizontal with an initial speed of `50m//s`. At the highest point in its trajectory, the projectile explodes into two fragments of equal mass, the first of which falls vertically with zero initial speed.
(a) How far from the point of firing does the second fragment strike the ground? (Assume the ground is level.)
(b) How much energy was released during the explosion?

Answer

(a) 360m, (b) 10800 J

Explanation

(a) Explosion will not chage the path of CM, therefore CM wll fall at a distance equal to range from point of projection.

`rArrx_(CM)=((m)/(2)x_(1)+(m)/(2)x_(2))/(m)=(1)/(2)(x_(1)+x_(2))`
`rArrR=(1)/(2)((R)/(2)+x)`
`x=(3R)/(2)=(3)/(2)((u^(2)sin2theta)/(g))=(3)/(2)((2500)(2)(4//5)(3//5))/((10))=360m`
(b) `"Energy released " ="finalenergy" - "initial energy"`
`=(1)/(2)(m)/(2)(2vcostheta)^(2)-(1)/(2)m(vcostheta)^(2)`
`=(1)/(2)mv^(2)cos^(2)theta`
`=(1)/(2)(24)(50xx50)((3)/(5))^(2)=10,800J`