An explosion breaks a rock into three parts in a horizontal plane two of them go off at right angles to each other the first part of mass 1 kg moves with a speed of 12 m/s the second part of mass 2kg moves with a speed of 8 m/s and the third aprt flies off with a speed of 4 m/s calculate the mass of third part

Options

A. 10 kg
B. 2.5 kg
C. 4 kg
D. 5 kg

Answer

d

Explanation

`m_(1) vec(v )_(1) + m_(2) vec(v )_(2) + m_(3) v_(3) = 0`
`:. |m_(3) vec(v )_(3) | = |-(m_(1) vec(v )_(1) + m_(2) vec(v )_(2))|`
`m_(3) v_(3) = sqrt(m_(1)^(2) v_(1)^(2) + m_(2)^(2) v_(2)^(2))`
`4m_(3) = sqrt(144+ 256) = sqrt(400) = 20`
Mas `m_(3) = (20)/(4) = 5kg`