Figure shows a sphere moving in a steady flow of air in the `x`-direction on a horizontal plane.The air stream exerts an essentially constant acceleration `1.8 m//sec^(2)` on the sphere in the `x`-direction.If at `t=0` the sphere is moving as shown in figure, determine the time `t` required for the sphere to cross the `y`-axis again.

Options

A. `1//3 sec`
B. `2//3 sec`
C. `4//3 sec`
D. `5//3 sec`

Answer

D

Explanation

The motion of the sphere is similar to projection motion.The components of its acceleration are `a_(x)=1.80m//s^(2),a_(y)=0`.When the sphere crosses the `y`-axis, its displacement component along `x`-axis is zero.`0=(v_(ix)t)+1/2a_(x)t_(2)`,
`0=3sin 30^(@)t-1/2(1.8)t^(2) or t=1.667 s`