Final answer:
To find the increase in the water temperature, the kinetic energy of the projectile is converted to thermal energy and then related to the specific heat capacity of water to calculate the temperature change, resulting in a small increase of approximately 0.05974°C.
Step-by-step explanation:
To determine the increase in water temperature when a 1.5 kg projectile traveling at 100 meters per second is completely stopped in water, we first calculate the kinetic energy of the projectile using the formula kinetic energy = (1/2) * mass * velocity2. Using a mass of 1.5 kg and a velocity of 100 m/s, we find that the kinetic energy is (1/2) * 1.5 kg * (100 m/s)2 = 7500 Joules.
Next, to find out how much this energy will heat the water, we use the specific heat capacity of water. Since the specific heat of water is given as 1 calorie per gram per degree Celsius, we first convert 30 kg of water to grams, which is 30,000 grams, and then convert the kinetic energy from Joules to calories (1 calorie = 4.184 Joules). Therefore, 7500 Joules is equivalent to approximately 1792.22 calories.
Now we use the specific heat formula, ΔT = Q / (m * c), where ΔT is the temperature change, Q is the heat energy, m is the mass, and c is the specific heat capacity. Plugging in the values, we get ΔT = 1792.22 cal / (30,000 g * 1 cal/g°C) = 0.05974°C as the increase in temperature of the water.