Five persons A, B, C, D and E are pulling a cart of mass $$100$$ kg on a smooth surface and cart is moving with acceleration $$3$$ $$m/s2$$ in east direction. When person A stops pulling, it moves with acceleration $$1$$ $$m/s2$$ in the west direction. When person B stops pulling, it moves with acceleration $$24$$ $$m/s2$$ 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

Question

Infinity Learn · Accepted Answer

When all are pullingF¯$$net=100$$×$$3i^$$     .......(1)when$$ A stopsF¯net−F¯$$A=100$$×$$1($$−$$i^)     .......$$(2)when$$ B stopsF¯net−F¯$$B=100$$×$$24j^$$         .......$$(3)from$$ these three get F¯$$A+F$$¯$$B=(700i^$$−$$2400j^)Nhence$$ acceleration of the carta→$$=F$$¯$$A+F$$¯$$Bm=(700i^$$−$$2400j^)100m/s2a$$→$$=(7i^$$−$$24j^)m/s2$$⇒|a→|$$=72+242=25m/s2$$

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