7 A helicopter is initially at rest on the ground at the origin when it begins to accelerate in a vertical plane. Its acceleration is \(( 4.2 \mathbf { i } + 2.5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\) for the first 20 seconds of its motion. The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal and vertical respectively. Assume that the helicopter moves over horizontal ground.

1. Find the height of the helicopter above the ground at the end of the 20 seconds.
2. Find the velocity of the helicopter at the end of the 20 seconds.
3. Find the speed of the helicopter when it is at a height of 180 metres above the ground.