- When a woman walks due North at a constant speed of \(4 \mathrm {~km} \mathrm {~h} ^ { - 1 }\), the wind appears to be blowing from due East. When she runs due South at a constant speed of \(8 \mathrm {~km} \mathrm {~h} ^ { - 1 }\), the speed of the wind appears to be \(20 \mathrm {~km} \mathrm {~h} ^ { - 1 }\).
Assuming that the velocity of the wind relative to the earth is constant, find
- the speed of the wind,
- the direction from which the wind is blowing.