6 A lorry of mass 16000 kg climbs a straight hill \(A B C D\) which makes an angle \(\theta\) with the horizontal, where \(\sin \theta = \frac { 1 } { 20 }\). For the motion from \(A\) to \(B\), the work done by the driving force of the lorry is 1200 kJ and the resistance to motion is constant and equal to 1240 N . The speed of the lorry is \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at \(A\) and \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at \(B\).

1. Find the distance \(A B\). For the motion from \(B\) to \(D\) the gain in potential energy of the lorry is 2400 kJ .
2. Find the distance \(B D\). For the motion from \(B\) to \(D\) the driving force of the lorry is constant and equal to 7200 N . From \(B\) to \(C\) the resistance to motion is constant and equal to 1240 N and from \(C\) to \(D\) the resistance to motion is constant and equal to 1860 N .
3. Given that the speed of the lorry at \(D\) is \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), find the distance \(B C\).