Trouble Finding Change in Temp Given KE = Q (Thermal Energy)

[Oannes]

Homework Statement

A 3kg projectilce traveling at 100 m/s is stopped by being shot into an insulated tank containg 100kg of water. If the KE of the projectile is completely convereted into thermal energy, how much will the temp of the water increase in degrees celcius? The standard heat of water is 1 cal/g C.

Homework Equations

Thermal Energy = mass * Specific Heat * change in temperature
Kinetic Energy = 1/2 * mass * Velocity²
KE = TE

The Attempt at a Solution

So did all my conversions to get like units below.

1cal/g C = 4.18J/.001kg * C (Specific Heat of Water)

Then solved for Kinetic Energy:

KE = 1/2 (3kg) (100m/s)²
KE = 15000kg m²/s² = 15000J

Then solved for Thermal Energy setting Kinetic equal to Thermal as it states in the problem:

15000J = 100kg (4.18J/.001kg C) * Change in Temp
15000J = 418000J/C * Change in Temp
.0359 C = Change in Temp

Now this seems to be my answer, and I think that maybe such a miniscule change could be my answer considering the circumstances, however I fear that I have done something wrong somewhere and cannot find it. Most of my problems so far have involved significant temperature change so I feel they are either changing things up or I have made a mistake somehwere. Is all my logic correct? or have I messed up somewhere? Also I understand this question could fall under physics, however they have us working this out in my Engineering and Problem Solving course. Thanks so much in advance.

 

[Bystander]

Is all my logic correct?

The only "correction" that might be applied is to include the heat capacity of the projectile; it hasn't been specified, and could be argued to be < 4 mK , the uncertainty of the experiment, or, included if you feel that it is necessary.