A 1.2 kg spring-activated toy slides on a smooth surface along the +x-axis with a speed of 0.5 m/s. At the origin, it explodes into two fragments. Fragment 1 has a mass of 0.4 kg and a speed of 0.9 m/s along the –z-axis. What is the angle θ made between the velocity vector of fragment 2 and the +x-axis?

Respuesta :

Answer:

Explanation:

mass, m = 1.2 kg

initial velocity, u = 0.5 m/s along X axis

[tex]\overrightarrow{u}=0.5\widehat{i}[/tex]

mass of first fragment, m1 = 0.4 kg

final velocity of the first fragment, v1 = 0.9 m/s along - Z axis

[tex]\overrightarrow{v_{1}}=-0.9\widehat{k}[/tex]

mass of second fragment, m2 = 1.2 - 0.4 = 0.8 kg

Let the final velocity of the second fragment is v2.

Use conservation of momentum

[tex]m\times \overrightarrow{u}=m_{1}\times \overrightarrow{v_{1}} + m_{2}\times \overrightarrow{v_{2}}[/tex]

[tex]1.2 \times 0.5 \widehat{i}=0.4 \times (-0.9\widehat{k})+ 0.8\times \overrightarrow{v_{2}}[/tex]

[tex]\overrightarrow{v_{2}}=0.75\widehat{i}+0.45\widehat{j}[/tex]

Angle made with X axis is 0 degree.