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Five person A, B, C, D and E are pulling...

Five person A, B, C, D and E are pulling a cart of mass 100 kg on a smooth surface and cart is moving with acceleration `3 m//s^(2)` in each direction. When person 'A' stops pulling, it moves with acceleration `1 m//s^(2)` in the west direction. When person 'B' stops pulling, it moves with acceleration `24 m//s^(2)` in the north direction. The magnitude of acceleration of the cart when only A and B pull the cart keeping their directions same as the old directions, is `(25//n) m//s^(2)`, value of `n` is:

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The correct Answer is:
1
`vec(F)_(A) + vec(F)_(B) + vec(F)_(C) + vec(F)_(D) + vec(F)_(E) = 300 hat(i)`....(i)
`vec(F)_(B) + vec(F)_(C) + vec(F)_(D) + vec(F)_(E) = - 100 hat(i)` ....(ii)
`vec(F)_(A) + vec(F)_(C) + vec(F)_(D) + vec(F)_(E) = 2400 hat(j)` .....(iii)
Eqn. (i) -Eqn. (ii) gives: `vec(F)_(A) = 400 hat(i)`
Eqn. (iii) - Eqn. (ii) gives : `vec(F)_(A) - vec(F)_(B) = 2400 hat(j) + 100 hat(i)`
`400 hat(i) - vec(F)_(B) = 2400 hat(j) + 100 hat(i)`
`vec(F)_(B) = 300 hat(i) - 2400 hat(j)`
When only person A and B pull the cart,
`vec(F)_(A) + vec(F)_(B) = 700 hat(i) - 2400 hat(j)`
`|vec(F)_(A) + vec(F)_(B)|/(m)`
`= (2500)/(100) = 25 m//s^(2)`
`:. n = 1`
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