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Question: Five persons A, B, C, D and E are pulling a cart of mass 100 kg on a smooth surface and cart is movi...

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/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/s2in 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 –

A

26 m/s2

B

371\sqrt{71}m/s2

C

25 m/s2

D

30 m/s2

Answer

25 m/s2

Explanation

Solution

When all are pulling

F→net=100×3i^{\overrightarrow{F}}_{net} = 100 \times 3\widehat{i} ...(1)

When 'A' stops

F→net−F→A=100×1(−i^){\overrightarrow{F}}_{net} - {\overrightarrow{F}}_{A} = 100 \times 1( - \widehat{i}) …(2)

When 'B' stops

F→net−F→B=100×24(j^){\overrightarrow{F}}_{net} - {\overrightarrow{F}}_{B} = 100 \times 24(\widehat{j}) …(3)

from these three get

F→A+F→B{\overrightarrow{F}}_{A} + {\overrightarrow{F}}_{B} and solve.