7. A machine fires ball-bearings up the line of greatest slope of a rough plane inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 3 } { 5 }\). The coefficient of friction between the ball-bearings and the plane is \(\frac { 1 } { 4 }\).

1. Show that the magnitude of the acceleration of the ball-bearings is \(\frac { 4 } { 5 } g\) and state its direction. Given that the machine is placed at a point \(A , 30 \mathrm {~m}\) from the top edge of the plane, and the ball-bearings are projected with an initial speed of \(20 \mathrm {~ms} ^ { - 1 }\),
2. find, giving your answer to the nearest cm , how close the ball-bearings get to the top edge of the plane.
3. How long does it take for a ball-bearing to travel from the highest point it reaches back down to the point \(A\) again? END