Thermo and Projectile Motion: Bathtub Bather Launch Calculation

If not, we can skip this part of the problem.In summary, we are given a person of mass 70.0 kg sitting in a bathtub with dimensions 190.0 cm by 80.0 cm and water at a temperature of 37.0 C. The volume of water is 0.152 m^3 and the mass is 152 kg. The energy released by cooling the water to form ice and launching the person vertically into the air is -7.433256 x 10^7 J.
  • #1
jbyrd5014
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Homework Statement


A person of mass 70.0 kg is sitting in the bathtub. The bathtub is 190.0 cm by 80.0 cm before the person got in, the water was 10.0 cm deep. The water is at a temperature of 37.0 C. Suppose that the water were to cool down spontaneously to form ice at 0.0 C, and that all the energy released was used to launch the hapless bather vertically into the air.

Homework Equations



The Attempt at a Solution



Density of Water = 1000 kg/m^3

Volume of water
1.9 * 0.8 * 0.1 = 0.152 m^3

Mass of water
0.152 m^3 * 1000 kg/m^3 = 152 kg

Energy of cooling water = mcT
152 * 4190 * (0-37) = 2.356456 x 10^7

Energy of freezing water = mL
-152 * 3.34*10^5 =-5.092 x 10^7

Sum of Energy
-7.433256 x 10^7nvm got it..
h=KE/mg
 
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  • #2
Have you learned about gravitational potential energy yet?
 

1. What is the difference between heat and temperature?

Heat is a form of energy that is transferred from one object to another due to a difference in temperature. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in an object.

2. How does heat transfer occur?

Heat transfer occurs through three main mechanisms: conduction, convection, and radiation. Conduction is the transfer of heat through direct contact between objects, convection is the transfer of heat through the movement of fluids, and radiation is the transfer of heat through electromagnetic waves.

3. What is the relationship between temperature and kinetic energy?

The higher the temperature, the higher the average kinetic energy of the particles in an object. This means that as the temperature increases, the particles move faster and with more energy.

4. What is projectile motion?

Projectile motion is the motion of an object that is thrown or projected into the air and then moves under the force of gravity. It follows a curved path known as a parabola.

5. What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by the initial velocity, angle of launch, air resistance, and the force of gravity. These factors determine the shape and distance of the parabola that the projectile follows.

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