Initial Velocity problem?

Question

A 7.27 g bullet is fired vertically into a 1.16 kg
block of wood.
The bullet gets stuck in the block, and the
impact lifts the block 0.39 m up. (That is, the
block - with the bullet stuck in it - rises
0.39 m up above its initial position, and then
falls back down.)
Given g = 9.8 m/s^2. What was the initial
velocity of the bullet? Answer in units of
m/s.

Answer 1

First, momentum is conserved

7.27*vb/1000=(1.16+7.27/1000)*vw
vb=1000*(1.16+7.27/1000)*vw/7.27

Where vb is the speed of the bullet and vw is the speed of the combined block and bullet after collision

After the collision, use energy
m*g*h=.5*m*vw^2
mass divides out and
vw=sqrt(2*g*h)
vw=(2*9.81*0.39)

vw=7.65 m/s

plugging into vb equation

vb=1228 m/s

j

Answer 2

hint, on the real the rate is 0. so which you're making V(t) = 0. You get an expression for t and toss it into s. you be responsive to that s(t) - S_0 is going to be your height, 550ft. attempt it, the end result's superb and clean (you derive Steve's answer).