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 of `3 m//s^(2)` in east direction. When person A stops pulling, it moves with acceleration `1 m//s^(2)` in the west direction. When person B stops pulling, it move with acceleration `24 m//s^(2)` in the north direction. The magnitude of acceleration of the cart, when only A and B pull the cart keeping their direction same as the old directions, is :

Options

A. `26 m//s^(2)`
B. `3 sqrt71 m//s^(2)`
C. `30 m//s^(2)`
D. `25 m//s`

Answer

D

Explanation

`vec(F)_(A) + vec(F)_(B) + vec(F)_(C ) + vec(F)_(D) = 100 xx 3 hat(i)` …..(1)
`vec(F)_(B) + vec(F)_(C ) + vec(F)_(D) = - 100 xx 1 hat(i)` …(2)
`vec(F)_(A) + vec(F)_(C ) + vec(F)_(D) = 100 xx 24 hat(j)` …..(3)
from (1), (2) & (3)
get `vec(F)_(A) + vec(F)_(B) = 700 hat(i) - 2400 hat(j) = m vec(a)`