Answer : The temperature when the water and pan reach thermal equilibrium short time later is, 
Explanation :
In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.


where,
= specific heat of aluminium = 
= specific heat of water = 
= mass of aluminum = 0.500 kg = 500 g
= mass of water = 0.250 kg = 250 g
= final temperature of mixture = ?
= initial temperature of aluminum = 
= initial temperature of water = 
Now put all the given values in the above formula, we get:


Therefore, the temperature when the water and pan reach thermal equilibrium short time later is, 
Answer:
so here it will move in circle with radius 4.06 cm
Explanation:
As we know that proton is moving towards west while the magnetic field is vertically upwards
So here the force on the proton must be perpendicular to the velocity
So here we have

so here we have

since force is perpendicular to the velocity so here it must be centripetal force
here we have

so we have



so here it will move in circle with radius 4.06 cm
Answer:
The y-component of the normal force is 45.74 N.
Explanation:
Given that,
Mass of the crate, m = 5 kg
Angle with hill, 
We need to find the y component of the normal force. We know that the y component of the normal force is given by :

So, the y-component of the normal force is 45.74 N. Hence, this is the required solution.