At what speed would one need to fire a lead project tile in order for its temperature to rise from 25°C to 36.9°C upon impact on a stationary object

55 m/s

Explanation:

If all kinetic energy is converted to heat:

½ mv² = mCΔT

v = √ (2CΔT)

v = √ (2 * 128 J/kg/K * (36.9°C - 25°C))

v = 55.2 m/s

Rounded to two significant figures, the speed is 55 m/s.