An 30 g rifle bullet traveling at 390 m/s buries itself in a 4 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the maximum vertical displacement of the pendulum (height). (g

Mass of bullet 30g=30/1000=0.03kg

Speed of bullet = 390m/s

Mass of pendulum is 4kg

Total mass of bullet and pendulum, = 4.03kg

Length of pendulum is L = 2.8m

Then, momentum is conserved

Momentum before collision = momentum after Collision

Mass of bullet * Velocity of bullet=combine mass of bullet and pendulum * velocity of pendulum

0.03*390=4.03*V

V=0.03*390/4.03

V=2.9m/s

Then the Kinetic energy of pendulum is given as

K. E=½mv²

K. E=½*4.03*2.9²

K. E=16.95J

conservation of energy states that energy can neither be created nor destroy but can be transferred from one form to another.

Let acceleration due to gravity be

g=9.81m/s²

The vertical displacement of the pendulum (h) = ?

Potential energy of the pendulum is given as

P. E=mgh

P. E=4.03*9.81*h

P. E=39.53h

So the P. E of the pendulum equals K. E of the pendulum

P. E=K. E

39.53h=16.95

h=16.95/39.53

h=0.43m

Knowing the height we can find the angle of the pendulum at the top of the swing:

θ=arcos (l-h) / l

θ=arcos (2.8-0.43) / 2.8

θ=arcos (0.8464)

θ=32.2°

From A we get the displacement along the horizontal axis:

The maximum vertical displacement is

x=h Sinθ

x=0.43 Sin32.2

x=0.23m

So the displacement are (0.23,0.43) m