Rain falls vertically at the speed of \(30~\text{m/s}.\) A woman riding a bicycle with a speed of \(10~\text{m/s}\) in the north-to-south direction. What is the direction in which she should hold her umbrella?
[given: \(\tan 16^{\circ}= 0.29, \& \tan 18^{\circ}= 0.33]\)
1. | \(16^{\circ}\) with the vertical, towards the north |
2. | \(18^{\circ}\) with the vertical, towards the north |
3. | \(16^{\circ}\) with the vertical, towards the south |
4. | \(18^{\circ}\) with the vertical, towards south |
In a harbor, the wind is blowing at the speed of \(72~\text{km/h}\), and the flag on the mast of a boat anchored in the harbor flutters along the \(\mathrm{N\text-E}\) direction. If the boat starts moving at a speed of \(51~\text{km/h}\) to the north, what is the direction of the flag on the mast of the boat?
1. | almost due north |
2. | almost due east |
3. | almost due west |
4. | almost due south |