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

Answer

A

Explanation

The magnitude of the force (from the string ) is `T=30N`
The x-component`=Tsintheta=30xx(3)/(5)=18N`
The y-component`=Tcostheta=30xx(4)/(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 acceleration `=(18N)/(2kg)=9(m)/(s^2)`
The y-component of the acceleration `=(4N)/(2kg)=2(m)/(s^2)`