Two enemy guns are placed at A and B at `10sqrt(3)km` apart horizontally . A shell is fired from A horizontally with velocity 10m/s. At the same time a shell of double the mass of shell at A is fired from B at an angle `60^(@)` with horizontal towards A with the same magnitude of initial velocity as that of A. Moving in the same vertical plane, two shells collide in air while sticking to each other and falling at the depest point of the valley C (neglect air resistance).

Find the magnitude of horizontal component of the displacement vector `(vecBC)` (inkm).

Options

A. 11.55
B. 5.77
C. 10.98
D. 6.12

Answer

b

Explanation

For A. `h_(1)=(1)/(2)g t^(2)`
For B `h_(2)=10sin 60^(@)t+(1)/(2)g t^(2)`
`10cos 60^(@)xxt+10xt=10sqrt(3)`