3 is the answer teeeeeeeeeheeeeeeeee
Answer:
The first part can be solved via conservation of energy.

For the second part,
the free body diagram of the car should be as follows:
- weight in the downwards direction
- normal force of the track to the car in the downwards direction
The total force should be equal to the centripetal force by Newton's Second Law.

where
because we are looking for the case where the car loses contact.

Now we know the minimum velocity that the car should have. Using the energy conservation found in the first part, we can calculate the minimum height.

Explanation:
The point that might confuse you in this question is the direction of the normal force at the top of the loop.
We usually use the normal force opposite to the weight. However, normal force is the force that the road exerts on us. Imagine that the car goes through the loop very very fast. Its tires will feel a great amount of normal force, if its velocity is quite high. By the same logic, if its velocity is too low, it might not feel a normal force at all, which means losing contact with the track.
Answer:
d = 39.7 km
Explanation:
initial position of the boat is 45 km away at an angle of 15 degree East of North
so we will have


after some time the final position of the boat is found at 30 km at 15 Degree North of East
so we have


now the displacement of the boat is given as



so the magnitude is given as


The energy stored by a system of capacitors is given by

where Ceq is the equivalent capacitance of the system, and V is the voltage applied.
In the formula, we can see there is a direct proportionality between U and C. This means that if we want to increase the energy stored by 4 times, we have to increase C by 4 times, if we keep the same voltage.
Calling

the capacitance of the original capacitor, we can solve the problem by asking that, adding a new capacitor with

, the new equivalent capacitance of the system

must be equal to

. If we add the new capacitance X in parallel, the equivalent capacitance of the new system is the sum of the two capacitance

and since Ceq must be equal to 4 C1, we can write

from which we find