Five persons A, B, C, D, and E, are pulling a cart of mass 100kg 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 `24m//s^(2)` in the north direction. The magnitude of acceleration of the cart when only A and B pull the cart keeping their direction, is:

Options

A. `26m//s^(2)`
B. `3sqrt(71)m//s^(2)`
C. `25m//s^(2)`
D. `30m//s^(2)`

Answer

C

Explanation

When all are pulling.
`vec(F)_(net)=100xx3hati` .
when `A` stop
`vec(F)_(net)-vec(F)_(A)=100xx1(-hati)` .
when `B` stop
`vec(F)_(net)-vec(F)_(B)=100xx24hatj` .
from these three get `vec(F)_(a)+vec(F)_(B)=(700hati-2400hatj)N` .
Hence, acceleration of the cart,
`vec(a)=(vec(F)_(A)+vec(F)_(B))/(m)=((700hati-2400hatj))/(100)m//s^(2)` .
`vec(a)=(7hati-24hatj)m//s^(2)implies|vec(a)|=sqrt(7^(2)+24^(2))=25m//s^(2)` .