An explosion blows a rock into three parts. Two pieces go off at right angles to each other; 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 (in kg).

Let m1, m2 and m3 be the masses of the three pieces. Given m1 =1.0 kg, m2 = 2.0 kgLet  v1 =12m/s, v2 =8m/ s, v3 =40 m/s. Let v1 and v2 be directed along x- and y-axes, respectively, and v3 be directed as shown.By the principle of conservation of momentum, initial momentum is zero. Hence, along x-axis: 0=m1v1−m3v3cos⁡θ along y-axis: 0=m2v2−m3v3sin⁡θ⇒m1v1=m3v3cos⁡θ and m2v2=m3v3sin⁡θBy squaring and adding, we get⇒ m32=12(12)2+(2)2(8)2(40)2⇒m3=0.5kg