Rifle Bullet Pendulum (Solved just on 1 aspect)

[KendrickLamar]

Homework Statement

A 36 g rifle bullet traveling 310 m/s buries itself in a 5.2 kg pendulum hanging on a 2m long string, which makes the pendulum swing upward in an arc. Determine the maximum vertical displacement of the pendulum (height)(g=9.8m/s^2)

Homework Equations

Pi = Pf
Law of conservation

The Attempt at a Solution

well i solved it out and I am pretty sure I am right, i found the velocity to be 2.131 m/s then plugged it into the law of conservation equation where the masses cancel out and you end up with 1/2(2.131)^2 = gh

h = .2318

but my question is because it says the pendulum hangs on a 2m long string, how does that impact the problem, do i subtract this height from the string? or vice versa? or add it?. I mean i know a pendulum is like a string or rod or w/e with a weight attached but the way its worded is like that there's an extra 2m string or something? does that impact the MAXIMUM vertical displacement at all? I'm just a little confused, thank you if u can help!

 

[HallsofIvy]

No, the "height" is the "height". The only thing the "2m long string" tells you is that the block will go upward on an arc of a circle with radius 2m (otherwise the block-bullet combination would just move laterally without ever stopping!). But the height is still given by "conservation of energy" (after the collision- since the bullet is imbedded in the block, that collision is a "perfectly inelastic" collision- energy is NOT conserved).

 

[KendrickLamar]

ah ok thank you sir!