A 2kilogram projectile traveling at 110 meters per second is

A 2-kilogram projectile traveling at 110 meters per second is stopped by being shot into an insulated tank containing 110 kilograms of water. If the kinetic energy of the projectile is completely converted into thermal energy with no energy lost, how much will the water increase in temperature in units of degrees Celsius? The specific heat of water is 1 calorie per gram per degree Celsius [cal/(g degree C)]. The temperature will increase by degree C. (Round your answer to three significant digits.)

Solution

Kinetic energy converted into thermal energy. So,

1/2m*V2 - 1/2 m *v2 = mCdelta(T)

The 2nd term is the final kinetic energy

If 2nd term is stopping of bullet then v = 0

So, 1/2*V^2 = C (dt), C=1000 in units of cal/kg*C)

dt = 1/2 *110^2 /1000 =6.050

This is the climb in the temperature 6.050 degrees. ( rounded up to 3 decimals)