Answer:
6.8 mm
Explanation:
We are given that
Mass of block,m=10 kg
Mass of bullet,[tex]m_b=10 g=10\times 10^{-3} kg[/tex]
1 kg=1000 g
Total mass of system,M=[tex]m+m_a=10+10\times 10^{-3}=10.01kg[/tex]
Speed of bullet,u=300 m/s
[tex]\theta=30^{\circ}[/tex]
By law of conservation of momentum
[tex]m_bucos\theta=Mv[/tex]
[tex]v=\frac{m_bvcos\theta}{M}=\frac{0.01\times 300cos30^{\circ}}{10.01}=0.259m/s[/tex]
According to law of conservation of energy
Change in kinetic energy of system=Change in potential energy of system
[tex]\frac{1}{2}Mv^2-0=Mgh-0[/tex]
[tex]\frac{1}{2}(10.01)(0.259)^2=10.01\times 9.8 h[/tex]
Where [tex]g=9.8 m/s^2[/tex]
[tex]h=\frac{(0.259)^2}{2\times 9.8}=0.0034m[/tex]
1m=100 cm
[tex]h=0.0034\times 100=0.34 cm[/tex]
Distance traveled by block=[tex]d=\frac{h}{sin\theta}=\frac{0.34}{sin30^{\circ}}=0.68 cm=6.8 mm[/tex]
1cm=10 mm
