A cannon shell is fired to hit a target at a horizontal distance `R`. However, it breaks into two equal parts at its highest point. One part `A` returns to the cannon. The other part is:

Options

A. Will fall at a distance `R` beyond the target
B. Will fall at a distance `3R` beyond the target
C. Will hit the target
D. Have nine times the kinetic energy of `A`

Answer

A, D

Explanation

From the figure
`sin theta=(R_(e))/(2R_(e))=1/2`
`theta=(pi^(c))/6`
During revolution satellite leaves two spherical patches `1` and `2` on the earth surface at North & due to curvature. The area of patches can be obtained by solid angles. solid angles subtended by a patch on the earth's centre is
`omega=2pi(1-cos theta)`
`omega=2pi(1-(sqrt(3))/2)`
`omega=pi(2-sqrt(3))`
Area of patch `1` & `2` is
`A_(P)=omegaR_(e)^(2)=pi(2-sqrt(3))R_(e)^(2)`
Total area on earthis surface to which communication can be made is
`A_(C)=4piR_(e)^(2)-2A_(P)`
`A_(C)=4piR_(e)^(2)-2pi(2-sqrt(3))R_(e)^(2)`
`A_(C)=2sqrt(3)piR_(e)^(2)`