Two particles A and B of mass 1 kg and 2 kg respectively are projected in the direction shown in figure with speeds `u_(A) = 200 ms^(-1)` and `u_(B) = 50 ms^(-1)`. Initially they were 90 m apart. Find the maximum height attained by the center of mass of the particles. Assume acceleration due to gravity to be constant. (Take, `g=10 ms^(-2)`.

Options

A. 5 meter
B. 10 meter
C. 25 meter
D. 20 meter

Answer

A

Explanation

Initially velocity of centre of mass of `(A + B)` system is
`u_(cm)=(1xx200-2 xx85)/(3)=10 m//s` upwards
`:.` maximum height attained by centre of mass above its initial position is
`H=(u_("cm")^(2))/(2g)=(100)/(2xx10)=5` metres