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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 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 14 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 –

A

26 m/s2

B

3713\sqrt{71}ms2

C

25 m/s2

D

30 m/s2

Answer

25 m/s2

Explanation

Solution

When all are pulling

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

When 'A' stops

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

When 'B' stops

F→net{\overrightarrow{F}}_{net} – F→B{\overrightarrow{F}}_{B} = 100 × 24j^\widehat{j}

from these three get

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