How can we solve the ballistic pendulum problem using conservation of energy?

[fairuzjannah]

Homework Statement

A ballistic pendulum consisting of a heavy bob of mass M suspended form a fixed point by a thread of length l is at rest. A bullet of mass m and traveling horizontally at a speed v hits the bob and imbeds itself an the bob. As a result, the pendulum is deflected through a amaximum angle θ from the vertical. Show that

v = (M+m)/m √(2gl(1-cos⁡〖θ)〗 )

where g is the acceleration du to gravity ?

Homework Equations

The Attempt at a Solution

i really blind with this questions, anyone please i need an answer how to solve it..thaanks :)

 

[HallsofIvy]

Well, as you suggest in your title, you can use "energy"- specifically, conservation of energy. (I don't believe you need conservation of momentum.)

Initially, the mass Mis not moving so its kinetic energy is 0 and the mass m has speed v so its kinetic energy is $(1/2)mv^2$. We can take the potential energy to be 0 at the initial height of bullet and bob so the total energy is $(1/2)mv^2$. After impact, at the bob's highest point, both bullet and bob have 0 kinetic energy so the total energy is just the potential energy, (m+M)g h where h is the height the bob and bullet rise to. By conservation of energy, then, $(m+M)gh= (1/2)mv^2$. Solve that for v.