Answer:
The problem involves finding the effect of added mass on the speed of a moving object, which can be determined using the law of conservation of momentum.
Before the snow starts falling, the initial momentum of the car is 5000 kg * 7.0 m/s = 35000 kg m/s.
As the snow falls, it adds mass to the car, and its momentum increases. The increase in momentum can be calculated as follows:
2.6 kg/min * 100 min = 260 kg
The final momentum of the system (car + snow) is given by:
35000 kg m/s + 260 kg * 0 m/s (since the snow is falling vertically and has no initial velocity relative to the car) = 35000 kg m/s + 260 kg * 0 m/s = 35000 kg m/s
The final velocity of the system (car + snow) can be determined by dividing the final momentum by the total mass:
35000 kg m/s / (5000 kg + 260 kg) = 35000 kg m/s / 5260 kg = 6.64 m/s
So the speed of the car after 100 minutes is 6.64 m/s.