A commander fires a shell at certain angle of projection from A which clears the building of dimensions `20xx15xx12.5m` in it's diagonal plane. Shell just clears the roof diagonally at points P and Q and falls on the other side of the building at B and makes angle `45^(@)` with the horizontal at P and Q as shown in the figure. If the range AB of the shell is `a^(2)xxsqrt(b)` then find b? (a and b lowest possible integers)

Answer

3

Explanation

`PQ=sqrt(15^(2)+20^(2))=25`
`25=(V_(P)^(2)sin(2xx45^(@)))/(g) implies V_(P)=5sqrt(10)m//s`
`v_(A)^(2)sin^(2)theta-2xx10xx12.5=(5sqrt(5))^(2)`
`impliesV_(A)sintheta=5sqrt(15)m//s`
`V_(A)costheta=V_(P)cos45^(@)=5sqrt(5)m//s "and" theta=60^(@)`
`AB=(V_(2)^(A)sin^(2)theta)/(g)=25sqrt(3)`