Five persons A, B, C, D & E are pulling a cart of mass 100 kg on a smooth surface and cart is moving

Question

Five persons A, B, C, D & E are pulling a cart of mass 100 kg on a smooth surface and cart is moving with acceleration 3 m/s2 in east direction. When person &#8242;A&#8242; stops pulling, it moves with acceleration 1m/s2 in the west direction. When person &#8242;B&#8242; stops pulling, it moves with acceleration 24 m/s2 in the north direction. The magnitude of acceleration of the cart when only A & B pull the cart keeping their directions same as the old directions, is :

Accepted Answer

        A + B + C + D + E = 300 i   ..........(1)
        B + C + D + E = − 100 i ...................    (2)
        A + C + D + E = 2400 j ...................    (3)
equation (1) - equation (3) give
        B = 300 i − 2400 j ..............................(4)
equation (1) - equation (2) give
        A = 400 i ........................................ (5)
Adding equation (4) and (5)
⇒    A + B = 700 i − 2400 j
        a_{(A + B)} =
         = 7 i − 24 j = 25 m/s²

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