A jet plane is flying with a constant speed along a straight line, at an angle of 25.5° above the horizontal, as Figure 4.30a indicates. The plane has weight vector W whose magnitude is 86500 N, and its engines provide a forward thrust vector T of 103000 N. In addition, the lift force vector L (directed perpendicular to the wings) is 78100 N and the air resistance vector R is 65800 N. Suppose that the pilot suddenly jettisons 3150 N of fuel. If the plane is to continue moving with the same velocity under the influence of the same air resistance vector R , by how much does the pilot have to reduce each of the following?
state which of the following are vectors and which are scalars distance, mass time, weight, volume ,density ,speed verbosity acceleration ,force,temperature and energy.
To determine how much the pilot needs to reduce each of the given quantities, we need to analyze the forces acting on the plane before and after jettisoning the fuel.
Before jettisoning the fuel, the forces acting on the plane can be resolved into their horizontal and vertical components:
1. Thrust vector T: This vector provides the forward motion of the plane. Since it is not affected by fuel jettisoning, the pilot does not need to reduce it.
2. Weight vector W: This vector acts vertically downward and is balanced by the lift force vector L acting vertically upward. Since the weight and lift forces remain the same, the pilot does not need to reduce either of them.
3. Air resistance vector R: This vector acts opposite to the motion of the plane. To counteract it and maintain the same velocity, the pilot needs to adjust the remaining force.
After jettisoning the fuel, the total force in the horizontal direction remains the same, so the pilot does not need to reduce any forces in that direction.
In the vertical direction, the weight of the fuel that was jettisoned is subtracted from the total weight. Thus, the pilot needs to reduce the lift force by the weight of the jettisoned fuel.
The weight of the jettisoned fuel is given as 3150 N. Therefore, the pilot needs to reduce the lift force by 3150 N to maintain the same velocity under the influence of the same air resistance vector R.