Question

1. draw a force diagram for a skydiver who has just left the plane and is accelerating toward the ground. force diagram: sign conventions: sum of forces equation(s): \\(\sum f_x =\\) \\(\sum f_y =\\) system schema: (skydiver) (earth) subscript definitions:

Explanation:

Step1: Analyze horizontal forces

Since there is no horizontal acceleration (assuming no wind - like horizontal forces mentioned), the sum of horizontal forces is zero.
$$\sum F_x = 0$$

Step2: Analyze vertical forces

The skydiver is accelerating downwards. The force of gravity \(F_g\) acts downwards (negative direction as per the sign convention if we assume up as positive) and the air resistance \(F_{air}\) acts upwards. According to Newton's second law \(F = ma\), and \(F_{net}=ma\). The net force in the vertical direction is \(F_g - F_{air}\) (taking down as negative if up is positive, but if we follow the sign convention where up is positive, then \(F_{air}\) is positive and \(F_g\) is negative. But more accurately, using the general form \(\sum F_y=F_{air}-F_g\) (if we consider the magnitude of forces and direction based on the sign - convention). However, if we assume the sign - convention where up is positive, and the skydiver is accelerating down (so \(a_y<0\)), then \(\sum F_y = F_{air}-F_g=ma_y\) (where \(m\) is the mass of the skydiver and \(a_y\) is the vertical acceleration). But if we just consider the force magnitudes and directions based on the sign - convention (up as positive), and since there is no information about other vertical forces, \(\sum F_y=F_{air}-F_g\)

Answer:

\(\sum F_x = 0\), \(\sum F_y=F_{air}-F_g\)