A balloon is tied to a block. The mass of the block is `2kg`. The tension of the string between the balloon and the block is `30N`. Due to the wind, the string has an angle `0` relative to the vertical direction. `costheta=4//5`and `sintheta=3//5`. Assume the acceleration due to gravity is `g = 10 m//s^(2)`. Also assume the block is small so the force on the block from the wind can be ignored. Then the x-component and the y-component of the acceleration a of the block.

Options

A. `9m//s^(2),2m//s^(2)`
B. `9m//s^(2),12m//s^(2)`
C. `18m//s^(2),2m//s^(2)`
D. `18m//s^(2),12m//s^(2)`

Answer

A

Explanation

The magnitude of the force (from the string) is `T=30N`.
The x-component `=T cos theta=30xx4//5=18N`.
The y-component `=T costheta=30xx4//5=24N`.
The total force on the block is:
the x-component`=18N`.
the y-component `=24-mg=24-20=4N`.
The x-component of the accelertion `=18N//2kg=9m//s^(2)`
The y-component of the acceleration `=4N//2kg=2m//s^(2)`