If
a.05 kg bullet is fired from a gun at 400m/s and hits a 1.3 kg block hanging from a sting .8-meters long, determine how high the block rises from the equilibrium position

If the following is given:

mass of bullet = 0.05kg
mass of block = 1.3 kg
speed of bullet = 400 m/s

After the hit, the bullet will stick to the block.

If the length of string = 8m, the block will go up to a height of approximately 11.2 m.

If the length of the string is only 0.8m the block can only reach a maximum height of 2 * 0.8 = 1.6m. 

Calculation:
1. Calculate the total momentum p = mv before the bullet hits the block
2. Momentum is conserved. Calculate the speed of the block and the bullet using the momentum from step 1.
3. Calculate the height by using the concept of conservation of energy:
1/2mv² = mgh
v is the speed from step 2
g = 9.81
m mass of the bullet and the block
h is the maximum height of the block and the bullet