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).

Question

Infinity Learn · Accepted Answer

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⇒ $$m32=12(12)2+(2)2(8)2(40)2$$⇒$$m3=0.5kg$$

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).

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!