Answer:
The initial kinetic energy of the bullet is closest to 491.87 J
Explanation:
Given;
mass of bullet, m₁ = 18g = 0.018kg
mass of block, m₂ = 10kg
height moved by the block, h = 9 mm = 0.009 m
time taken for the bullet to travel through the block, t = 0.001s
let the initial velocity of the bullet = v₁
let the final velocity of the bullet = v₂
Apply the principle of conservation of linear momentum;
initial momentum = final momentum
0.018v₁ = v₂(0.018 + 10)
0.018v₁ = 10.018v₂ -----equation (1)
Apply the law of conservation of energy when the bullet lifts the block through 9mm
mgh = ¹/₂mv₂²
gh = ¹/₂v₂²
v₂² = 2gh
v₂ = √2gh
v₂ = √(2 x 9.8 x 0.009)
v₂ = 0.42 m/s
Substitute in v₂ in equation 1, to determine the initial velocity of the bullet;
0.018v₁ = 10.018v₂
0.018v₁ = 10.018(0.42)
0.018v₁ = 4.208
v₁ = 4.208 / 0.018
v₁ = 233.78 m/s
Now, determine the initial kinetic energy of the bullet;
K.E₁ = ¹/₂m₁v₁²
K.E₁ = ¹/₂(0.018)(233.78)²
K.E₁ = 491.87 J
Therefore, the initial kinetic energy of the bullet is closest to 491.87 J
