John’s mass is 91.2 kg, and barbara’s is 51.9 kg. he is standing on the x axis at xj = +9.99 m, while she is standing on the x axis at xb = +3.27 m. they switch positions. how far and in which direction does their center of mass move as a result of the switch?

the center of gravity moves by 1.9 m towards the origin

Explanation:

from the question we are given the following

John's mass (Mj) = 91.2 kg

Barbara's mass (Mb) = 51.9 kg

John's location (Xj) = + 9.99 m

Barbara's location (Xb) = +3.27 m

center of mass (X) = ?

the center of mass is where the masses of John and Barbara is concentrated, and it is given by the formula below

X = ( ( Mj x Xj ) + ( Mb x Xb ) ) / (Mj + Mb)

X = ( ( 91.2 x 9.99 ) + ( 51.9 x 3.27 ) ) / ( 91.2 + 51.9 )

X =  7.6 m

now when they switch positions their locations now become

John's location (Xj) = + 3.27 m

Barbara's location (Xb) = +9.99 m

now putting their new locations into the formula

X = ( ( 91.2 x 3.27 ) + ( 51.9 x 9.99 ) ) / ( 91.2 + 51.9 )

X =  5.7 m

therefore the center of mass moves by

7.6 - 5.7 = 1.9 m

the center of gravity moves by 1.9 m towards the origin

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