At what speed should a lead bullet fly so that when it hits the wall it heats up by 120 degrees

At what speed should a lead bullet fly so that when it hits the wall it heats up by 120 degrees, if 20% of the bullet’s energy is converted into heat on impact.

Initial data: Δt (increase in the temperature of the lead bullet) = 120 ºС; η (percentage of heat that has passed from kinetic energy to heat) = 20% or 0.2.

Reference values: C (specific heat of lead) = 140 J / (kg * K).

The speed at which the bullet was supposed to fly, we determine from the equality: η * Ek = Q.

η * 0.5 * m * V ^ 2 = C * m * Δt.

V ^ 2 = 2C * Δt / η.

V = √ (2C * Δt / η).

Calculation: V = √ (2 * 140 * 120 / 0.2) = √168000 ≈ 410 m / s.

Answer: The lead bullet will have to fly at a speed of 410 m / s.