Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te
mperature and that of its surroundings. If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equals 0.4. Suppose the ambient temperature TA(t) is equal to a constant 38 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object. (a) dT dt = $$ Correct: Your answer is correct. 0.4(38-T) Suppose the ambient temp TA(t) = 38cos( π 30 t) degrees Celsius (time measured in minutes). Write the DE that describes the time evolution of temperature T of the object. (b) dT dt = Correct: Your answer is correct. If we measure time in hours the differential equation in part (b) changes. What is the new differential equation? Use the letter s to denote time in hours. (c) dT ds = If we measure time in hours and we also measure temperature in degrees Fahrenheit, the differential equation in part (c) changes even more. What is the new differential equation? Use the letter F to denote temperature in degrees Fahrenheit.
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Answer:
Explanation:
Given
The velocities of the protons are 400 m/s and 450 m/s
Mass of the Proton is
Since they travel in the opposite direction, therefore, their momentum cancels out each other.
Momentum is the product of mass and velocity
The direction of momentum is in the direction of proton having 450 m/s velocity.