Molecular Physics | Thermodynamics Answers

So I was thinking about Hawking's claim that matter entering a black hole is destroyed, which obviously violates our first law of thermodynamics. My question is why can't hawking be right and wrong at the same time? Imagine there are two barrels. A red and blue. There are an equal number of apples in each(5). If I remove a apple the red barrel and put it in the blue barrel, is the apple still apart of the red barrel bundle or is it now considered part of the blue? So why would the same not apply here. The law prevents matters destruction in this universe, but if the matter is no longer a part of this universe, would the law still prevent it from being destroyed? Is it the law preventing the destruction or is it the matter preventing the destruction? If a black hole was a entrance or exit to some place outside of our universe, wouldn't hawking be both correct and wrong at the same time? Can matter be destroyed as long as its not apart of the system it originated from?

While passing a slower car on the highway, you accelerate uniformly from 17.4 m/s to 27.3 m/s in a time of 10.0 s. How far do you travel during this time? What is your acceleration magnitude?

A Cessna aircraft has a lift-off speed of
112 km/h.
What minimum constant acceleration does
this require if the aircraft is to be airborne
after a take-off run of 253 m?
Answer in units of m/s2

An airplane flies 200 km due west from city A to city B and then 320 km in the direction of 25.0° north of west from city B to city C.
(a) In straight-line distance, how far is city C from city A?
(b) Relative to city A, in what direction is city C?
(c) Why is the answer only approximately correct?

What is the mass of water required to fill a circular hot tub 2.4 meters in diameter and 1.2 meters deep answer in units of kilograms?

What is the total translational KE of the atoms if the balloon has a diameter 39.0 cm at 46.0 °C and the pressure inside the balloon is 121.6 kPa?

how can I determine state equation if I have Gibbs potential. I know how to determine other potentials.
Problem says:
Gibbs free energy is G(p,T)=T^2ln(a*p/T), p is a preassure, T tempreature, an a constant.
Determine equation of state f(p,V,T). V is a volume.
I have no idea where to start.
Please help

Sally travels by car from one city to another. She drives for 28.0 min at 79.0 km/h, 49.0 min at 31.0 km/h, and 49.0 min at 70.0 km/h, and she spends 10.0 min eating lunch and buying gas.
Determine the average speed for the trip.

a metals feels colder to touch than wood kept in a cold place

why newton rings are circular