1. A hot-air balloon is rising vertically 19 ft/sec while the wind is blowing horizontally at 13 ft/sec. Find the speed v of the balloon and the angle θ it makes with the horizontal.
2. Two perpendicular forces act on a ring at the end of a chain that passes over a pulley and holds a crate. What is the weight of the crate if the horizontal force pulls at 47 pounds and the vertical force pulls at 40 lb?
3. An airplane has an airspeed of 430 km/h bearing 42° north of east. The wind velocity is 40 km/h in the direction 25° north of west. Find the resultant velocity representing the path of the airplane with respect to the ground. What is the actual ground speed of the aircraft in km/h?