An explosion blows a rock into three pieces Two pieces whose masses are 200 kg and 100 kg go off at `90^(@)` to eachother with a velocity of `8 m//s ` and ` 12 m//s ` respectively If the third piece flies off with a velocity of` 25 m//s` then calculate the mass of this piece and indicate the direction of flight of this piece in a diagram.

Explanation

Here , ` m_(1) = 200 kg , upsilon_(1) = 8 m//s `
`m_(2) = 100 kg , upsilon_(2) = 12 m//s`
`upsilon_(3) 25 m//s , m_(3) = ? `
`vec(p_(1)) = m_(1) vec(upsilon_(1)) = 200 xx 8 = 1600 kg m//s` , along OB
`vec(p_(2)) = m_(2) vec (upsilon_(2)) = 100 xx 12 = 1200 kg m//s` , along OA
Resultant momentum of these two pieces
`p = sqrt(p_(1)^(2)+ p_(2)^(2)) = sqrt((1600)^(2) + (1200)^(2)`
` = 2000 kg m//s `
If `theta` is angle made by `vec(p)` with `vec(OA)` , then
`tan theta = p_(1)/(p_(2)) = (1600)/(1200) = 1.33 `
`theta = tan^(-1) (1.33) = 53^(@)`
From `p = m_(3) upsilon_(3)`
`m_(3) = (p)/(upsilon_(3)) = (2000)/(25) = 80 kg `