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

Explanation:

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

energy can be converted from one form to another, but it cannot be created or destroyed in ordinary chemical or physical means. do not understand what you are asking but hope this