Desperate!!!!

A hot hair balloon is rising vertically 20 ft/sec while the wind is blowing horizontally at 15 ft/sec. Find the speed v of the balloon and the angle x it makes with the horizontal. I know how to solve this problem, but I don't understand why or how you kn...

An airplane has an airspeed of 150 km/hr. It is to make a flight in a direction of 70 degrees while there is a 25 km/hr wind from 340 degrees. What will the airplane's actual heading be? Please Explain this Problem to me!!!!

A blast blows a rock straight up at 150 ft/sec. The path of the rock is described by the s(t) = 150t-16t^2 where s is measured in feet and t in seconds. Find the velocity of the rock when it is 200 ft above the ground and when the rock hits the ground.