Answer to Question #102922 in Classical Mechanics for Patrick Kariuki

Question

A projectile of mass 56kg is moving at a constant speed of 8 m/s when it explodes into three pieces A, B and C. A(20 kg) flies along at 20 m/s along the line of flight and B(16 kg) flies at 15 m/s at 45 degrees to the line of flight in the forward direction. Find the velocity of mass C in magnitude and direction and estimate the energy supplied in the explosion.

Answer 1

As per the question,

the mass of the obje ct =56kg

initial velocity of the object = 8m/sec

let before the explosion, object was moving in the x axis.

After the explodes,

mass of A=20kg

velocity of the piece A=20m/sec along the x axis

mass of the piece B=16kg

velocity of the piece B=15m/sec

B is moving at 45 with x axis.

Mass of the object c=56-20-16=20 kg

let the velocity of the c = $v$

let C is moving at an angle $\theta$ with the horizontal.

Now applying the conservation of linear momentum

$56\times 8=20\times20+16\times 15 \cos 45+20\times v\cos\theta$

$488=400+120\sqrt{2}+20v\cos\theta$

$v\cos\theta=88-120\sqrt{2}--------(i)$

Similarly,

$20v\sin \theta=16\times\sin 45------------(ii)$

equation (ii) is dividing by equation (i)

$\tan\theta=\dfrac{4\sin 45}{5(88-120\sqrt{2})}$

$\tan\theta=-0.007$

$\theta=0.4^\circ$

$v\cos\theta=88-120\sqrt{2}$

$v\cos\theta=\dfrac{88-120\sqrt{2}}{\cos (0.4)}=-81.70 m/sec$

So, piece C will move along the negative x axis with the velocity -81.7 m/sec