To find the speed of the bullet, we can use the principle of conservation of mechanical energy. The potential energy at the maximum angle is equal to the initial kinetic energy of the bullet.
1. Calculate the potential energy at the maximum angle:
The potential energy is given by the formula: PE = mgh
where m is the mass of the block (2.1 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (0.0873 m).
Substituting the values into the formula, we get:
PE = (2.1 kg) * (9.8 m/s^2) * (0.0873 m) = 1.811 J
2. Use the principle of conservation of mechanical energy:
The initial kinetic energy of the bullet is equal to the potential energy when the block reaches the maximum angle.
The kinetic energy is given by the formula: KE = 0.5 * m * v^2
where m is the mass of the bullet (0.015 kg) and v is the velocity we want to find.
Equating the potential energy to the initial kinetic energy, we have:
1.811 J = 0.5 * (0.015 kg) * v^2
Simplifying the equation, we get:
v^2 = (2 * 1.811 J) / (0.015 kg)
v^2 = 241.47 m^2/s^2
Taking the square root of both sides, we find:
v ≈ 15.53 m/s
Therefore, the speed of the bullet is approximately 15.53 m/s.