Question

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 $3m/s^2$ in east direction. When person ‘A’ stops pulling, it moves with acceleration $1m/s^2$ in the west direction. When only person ‘B’ stops pulling, it moves with acceleration $24m/s^2$ 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 $\left(\frac{25}{n}\right)m/s^2$, value of n is

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Answer 1

When all are pulling
$\stackrel{\rightharpoonup }{F_{net}}=100\times 3\hat{i}\dots \dots \left(1\right)$
When ‘A’ stops
$\stackrel{\rightharpoonup }{F_{net}}-\stackrel{\rightharpoonup }{F_A}=100\times 1(-\hat{i})\dots \dots \left(2\right)$
When ‘B’ stops
$\stackrel{\rightharpoonup }{F_{net}}-\stackrel{\rightharpoonup }{F_B}=100\times 24\hat{j}$
From these three get
$\stackrel{\rightharpoonup }{F_A}+\stackrel{\rightharpoonup }{F_B}$ and solve