Question

An explosion breaks a rock into three parts. Two pieces go off at right angles to each other with 1.0 kg piece with a velocity of 12 m/s and other 2.0 kg piece with a velocity of 8 m/s. If the third piece flies off with a velocity of 40 m/s, compute the mass of the third piece.

• A. 0.5 kg
• B. 3 kg
• C. 0.7 kg
• D. 0.25kg

Answer 1

The correct option is A 0.5 kg



Let $m_1,m_{2}and{m}_3$ be the masses of the three pieces. $m_1=1.0kg,m_2=2.0kg$
Let $v_1=12m/s,v_2=8m/s,v_3=40m/s.Let{v}_{1}and{v}_2$ be directed along x-and y-axes, respectively, and $v_3$ be directed as shown.
By the principle of conservation of momentum, initial momentum is zero. Hence,
along x-axis: $0=m_1{v}_1-m_3{v}_{3}cos\theta$
Along y - axis: $0=m_2{v}_2-m_3{v}_{3}sin\theta$
$\Rightarrow m_1{v}_1-m_3{v}_{3}cos\theta and{m}_2{v}_2-m_3{v}_{3}sin\theta$
By squaring and adding, we get
$m_1^2{v}_1^2+m_2^2{v}_2^2=m_3^2{v}_3^2$
$\Rightarrow m_3^2=\frac{1^2(12{)}^2+(2{)}^2(8{)}^2}{(40{)}^2}\Rightarrow m_3=0.5kg$