Final answer:
The range of a projectile is zero at an angle of 90°. The maximum range for this optimal angle is marked as 45°. For thermal equilibrium, the temperature of all items in contact is the same (150 °C in the given scenario), and the maximum resistance of two resistors in series totaling 140 Ω is possible.
Step-by-step explanation:
The range of a projectile is defined as the horizontal distance which it travels while in motion. When a projectile is launched vertically upwards at an angle of 90°, it has no horizontal component of velocity, so its range is zero. Thus, the angle of a projectile for which its range is equal to zero would be at 90° (straight up). Conversely, the optimum angle for a projectile to achieve the maximum range is 45°, which splits the initial velocity equally between the horizontal and vertical components, utilizing both gravity and inertia to cover the greatest horizontal distance.
When considering thermal equilibrium, if a pan of oil is in thermal contact with a hot plate and both are in equilibrium, the temperature of the oil will be the same as the hot plate. Therefore, if the hot plate is at 150 °C, the oil will also be at 150 °C.
The maximum resistance possible when combining two resistors in series—where their resistances add—is achieved by summing the individual resistances. Given a resistor of 100 Ω and another of 40 Ω, the maximum possible resistance when these are connected in series is 140 Ω.
To determine which of the two solid spheres (A and B) is bigger when they have reached thermal equilibrium, one would need additional information about their heat capacities, masses, or specific heat, because the bigger sphere would have absorbed or released more heat to reach the equilibrium temperature.
For the Reaumur scale conversion to Celsius, if 100 °C equals 80 °R, then we can derive a conversion formula where the temperature in degrees Celsius is equal to the temperature in degrees Reaumur multiplied by 1.25 (T°C = T°R * 1.25).