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. 2/3sec
C. 4/3sec
D. 5/3sec

Answer

d

Explanation

The motion of the sphere is similar to projection motion. The components of its accelration 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)/(2)a_(X)t_(2)`,
`0=3sin30^(@)t-(1)/(2)(1.8)t^(2)` or `0=3sin 30^(@)t-(1)/(2)(1.8)t^(2)` or `t=1.667s`