1. A ship sailing on the open sea leaves Port A for Port B at a bearing of N25oW. A wind of 6 km/h on a bearing of N10oE blows the ship off course. If the ship is capable of 35 km/h in still water, find the new speed and direction relative to the shore.

2. A boat is capable of 20 km/h in still water. You wish to cross the river to a point directly across from your present position. At what angle to the bank should you steer the boat if the current is 8 km/h?

3. A boat is capable of 20 km/h in still water. You wish to cross the river downstream so that the angle the boat's push makes with the bank is 50o. At what angle to the bank should the boat steer if the current is 8 km/h? How long will it take to cross if the river is 1.7 km wide?

4. A boat is capable of 20 km/h in still water. You wish to cross the river to a point 0.6 km upstream from your present position. If the current is 8 km/h and the river is 1.5 km wide, at what angle to the bank should you steer the boat? How long will it take you to cross?

5. An aircraft is currently on course flying from A to B, a distance of 400 km, on a bearing of S20oE at 350 km/h. A 50 km/h wind blowing S80oE starts to blow the aircraft off-course. At what new bearing should the pilot steer in order to stay on course? What will the new speed be after the course correction?

6. You wish to swim across a river that is 0.3 km wide to a point directly across from your present position. If you can swim at a constant speed of 4 km/h in still water and the current is 2.5 km/h, at what angle to the bank should you swim so that you end up directly across on the other side ( i.e. your actual path is 90o to the bank)? What is your speed relative to the bank?

7. Three coplanar forces of 10 N, 20 N and x N act on a body and maintain it in a state of equilibrium. The x force acts along the horizontal and the 10 N force at...

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