Final answer:
a. The net horizontal force on the hot-air balloon is 4 N in the direction the wind is blowing.
b. The net vertical force is 1000 N upwards.
c. The net force is a combination of both horizontal and vertical forces acting on the balloon.
Step-by-step explanation:
In analyzing the free-body diagram of a hot-air balloon, the net horizontal and vertical forces, as well as the overall net force, can be determined based on the forces shown in the diagram. Given the forces such as Fl (lift), Fa (air resistance), and Fg (gravity):
- Fl = 4000 N is the upward buoyant force due to the difference in air density inside and outside the balloon.
- Fa = 2000 N is the air resistance acting against the balloon's ascent.
- Fg = 3000 N is the gravitational force pulling the balloon downwards.
As per the problem statement:
a. The net horizontal force exerted on the balloon is determined by the difference between the wind force (Fw) and the force of the current (Fc), which is
Fw - Fc = 4.0 N
This implies that if the wind is stronger than the current, the balloon will move horizontally in the direction of the wind.
b. The net vertical force exerted on the balloon can be calculated as the difference between the buoyant force (Fl) and the force of gravity (Fg). Since Fl = 4000 N and Fg = 3000 N, the net vertical force is
4000 - 3000 = 1000 N upwards.
c. The net force acting on the hot-air balloon combines both horizontal and vertical components. However, without precise direction vectors, we can't directly add these numerical values together. However, it is understood the overall net force consists of the horizontal net force plus the vertical net force.
Your question is incomplete, but most probably your full question can be seen in the attachment.