6 A small ball \(B\) is projected with speed \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of elevation \(30 ^ { \circ }\) from a point \(O\) on a horizontal plane, and moves freely under gravity.
- Calculate the height of \(B\) above the plane when moving horizontally.
\(B\) has mass 0.4 kg . At the instant when \(B\) is moving horizontally it receives an impulse of magnitude \(I \mathrm { Ns }\) in its direction of motion which immediately increases the speed of \(B\) to \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). - Calculate \(I\).
For the instant when \(B\) returns to the plane, calculate
- the speed and direction of motion of \(B\),
- the time of flight, and the distance of \(B\) from \(O\).