A rainstorm produces raindrops each with a mass of 7.5 × 10-5 kg and a terminal speed of 25 m/s. Suppose the rain is falling straight down (no wind).(a) [1 mark]What is meant by "terminal speed" and why does it exist?(b) [1 mark]While falling at terminal speed each rain drop is losing gravitational potential energy without gaining kinetic energy. Explain this in the context of conservation of energy.(c) [1 mark]Calculate the magnitude of the momentum of each rain drop. Suppose 560 drops of rain strike each square metre of ground every second. Consider a person stuck out in the rain. The top of their head has a cross-sectional area of 350 cm2.(d) [3 marks]Calculate the force of the rain hitting the person's head, assuming each rain drop comes to a stop?(e) [2 marks]Calculate the resulting pressure. Suppose a horizontal wind springs up giving the raindrops a horizontal velocity of 14 m/s, without changing their vertical velocity.(f) [2 marks]Calculate the momentum of a raindrop now, remembering that momentum is a vector quantity.

(a) Terminal speed is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration. This speed happens when the force due to gravity is equal to the drag force acting on the object.

(b) While falling at terminal speed, each raindrop is losing gravitational potential energy without gaining kinetic energy because the energy is being transferred into other forms, such as heat and sound, due to the interaction with the air molecules. This is in line with the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed.

(c) The magnitude of the momentum of each raindrop can be calculated using the formula p=mv, where m is the mass and v is the velocity. So, p = (7.5 × 10^-5 kg) * (25 m/s) = 0.001875 kg*m/s.

(d) The force of the rain hitting the person's head can be calculated using the formula F=dp/dt, where dp is the change in momentum and dt is the change in time. If each raindrop comes to a stop, the change in momentum is just the momentum of each raindrop. The number of raindrops hitting the person's head per second is the raindrop rate times the area of the person's head. So, F = (0.001875 kg*m/s * 560 drops/m^2 * 0.035 m^2) / 1 s = 0.03675 N.

(e) The pressure can be calculated using the formula P=F/A, where F is the force and A is the area. So, P = 0.03675 N / 0.035 m^2 = 1.05 Pa.

(f) The momentum of a raindrop now can be calculated using the Pythagorean theorem, since momentum is a vector quantity. The vertical momentum is still 0.001875 kgm/s, and the horizontal momentum is (7.5 × 10^-5 kg) * (14 m/s) = 0.00105 kgm/s. So, the total momentum is sqrt((0.001875 kgm/s)^2 + (0.00105 kgm/s)^2) = 0.00215 kg*m/s.