Model and solve problems that involve displacement, force, velocity and relative velocity using the above concepts.

A helicopter is moving with velocity \(\vec{v}_H = 40\vec{i} + 20\vec{j}\) km/h, where \(\vec{i}\) points east and \(\vec{j}\) points north. A wind has velocity \(\vec{v}_W = -15\vec{i} + 10\vec{j}\) km/h. a) Determine the velocity of the helicopter relative to the ground. (1 mark) b) Determine the speed of the helicopter relative to the ground, correct to one decimal place. (1 mark) c) Determine the direction of the helicopter relative to the ground as a bearing, correct to the nearest degree. (1 mark)

A helicopter is flying due north at a constant velocity of 45 m/s relative to the ground. A passenger drops a package horizontally with velocity 12 m/s due east relative to the helicopter. What is the magnitude of the velocity of the package relative to the ground?