Answer:
v = ((m + M) / m)*√(2*g*h)
Explanation:
Given
m = mass of the projectile
M = mass of the ballistic pendulum
v = initial speed of the projectile
v' = speedof the system (pendulum + projectile) after the inelastic collision
h = maximum height reached for the system
Knowing that is an inelastic collision we have
m*v + M*(0) = (m+M)*v'
⇒ v' = m*v / (m+M)
After the collision, we apply the Principle of the Conservation of Energy
Ki + Ui = Kf + Uf
where
Ui = Kf = 0 J
then
Ki = Uf
0.5*(m+M)*v'² = (m+M)*g*h
⇒ 0.5*v'² = g*h
⇒ v'² = 2*g*h
⇒ (m*v / (m+M))² = 2*g*h
⇒ v = ((m+M) / m)*√(2*g*h)