Answer:
68cm
Explanation:
You can solve this problem by using the momentum conservation and energy conservation. By using the conservation of the momentum you get
[tex]p_f=p_i\\mv_1+Mv_2=(m+M)v[/tex]
m: mass of the bullet
M: mass of the pendulum
v1: velocity of the bullet = 410m/s
v2: velocity of the pendulum =0m/s
v: velocity of both bullet ad pendulum joint
By replacing you can find v:
[tex](0.038kg)(410m/s)+0=(0.038kg+4.2kg)v\\\\v=3.67\frac{m}{s}[/tex]
this value of v is used as the velocity of the total kinetic energy of the block of pendulum and bullet. This energy equals the potential energy for the maximum height reached by the block:
[tex]E_{fp}=E_{ki}\\\\(m+M)gh=\frac{1}{2}mv^2[/tex]
g: 9.8/s^2
h: height
By doing h the subject of the equation and replacing you obtain:
[tex](0.038kg+4.2kg)(9.8m/s^2)h=\frac{1}{2}(0.038kg+4.2kg)(3.67m/s)^2\\\\h=0.68m[/tex]
hence, the heigth is 68cm
