Question

# A pendulum consists of a 5.2 kg ball suspended by a 1.3 m length of string...

A pendulum consists of a 5.2 kg ball suspended by a 1.3 m length of string with negligible mass and is initially at rest. A 4.4 g bullet travelling at 680 m/s is fired horizontally into the ball and is lodged there. The ball and bullet rise together to a maximum height of h. How long does it take from the moment of impact for the ball to first reach its maximum height?

momentum before bullet struck the ball Pi = m*vo

momentum after bullet struck the ball Pf = ( M +m)v

total momentum is conserved

momentum before collision = moemntum after collision

Pi = Pf

m*vo = (M+m)*v

4.4*10^-3*680 = ( 5.2 + (4.4*10^-3) )*V

speed of bullet + ball = 0.575 m/s <<<---answer

after the bullet is struck

total energy of the bullet + ball Ei = (1/2)*(M+m)*v^2

the bullet + block system reaches a height h

at the height h energy

Ef = (M + m)*g*h

total energy is conserved

Ef = Ei

(M+m)*g*h = (1/2)*(M+m)*v^2

h = v^2/(2g)

h = 0.575^2/(2*9.81)