The CM of an empty 1150 kg car is 2.35 m behind the front of the car.
How far from the front of the car will the CM be when two people sit in the front seat 2.70 m from the front of the car, and three people sit in the back seat 3.75 m from the front? Assume that each person has a mass of 80.0 kg.
express answer in proper significant figures and proper rounding of digits.

The CM of car with all people seated will be 2.60 m far from the front of the car.

Explanation:

Taking the front of the car as reference:

m₁x₁ + m₂x₂ + m₃x₃ = mx

here,

m₁ = mass of empty car = 1150 kg

x₁ = distance of CM of empty car from front = 2.35 m

m₂ = mass of 2 people sitting in front = 2 x 80 kg = 160 kg

x₂ = distance of CM of 2 people sitting in front from the front = 2.7 m

m₃ = = mass of 3 people sitting in back seat = 3 x 80 kg = 240 kg

x₃ = distance of CM of 3 people sitting in back seat from the front = 3.75 m

m = total mass of car with all people = 1150 kg + 160 kg + 240 kg = 1550 kg

x = distance of CM of car from front when all are seated = ?

Therefore,

(1150 kg)(2.35 m) + (160 kg)(2.7 m) + (240 kg)(3.75 m) = (1550 kg)x

x = 4043.5 kg.m/1550 kg

x = 2.60 m

3. dark matter

empty space could also be a simple vacuum

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