Question

At the top of trajectory,a mortar shell exploded into two fragment a 2.5kg piece moves south west with a horizontal velocity of 100m/s while 3.5kg piece moves north with a horizontal velocity of 70m/s.what was the horizontal direction of the cell just before explosion?

Answer 1

From the conservation of momentum:

$$(m_1+m_2)\bold{v}=m_1\bold{v_1}+m_2\bold{v_2}$$

$$(2.5+3.5)(v_x,v_y)=2.5(100\cos{45},-100\sin{45})+3.5(0,70)$$

$$(v_x,v_y)=(29.46,11.37)\frac{m}{s}$$

$$v=\sqrt{29.46^2+11.37^2}=31.6\frac{m}{s}$$

$$\theta=\arctan{\frac{11.37}{29.46}}=21.1\degree\ N\ of\ W$$