Question

at the instant shown, a paper airplane is moving horizontally to the right. the air exerts two independent forces on the plane: an upward lift force with magnitude less than the planes weight and a resistive drag force. which of the following correctly describes the change in velocity, if any, of the plane in the horizontal and vertical directions at this instant?
horizontal vertical
a no change no change
b no change increasing downward
c decreasing no change
d decreasing increasing downward
a a
b b
c c
d d

Explanation:

Step1: Analyze horizontal direction

According to Newton's second law \(F = ma\). In the horizontal direction, there is a resistive drag force. Since \(F_{drag}
eq0\), then \(a_{x}=\frac{F_{drag}}{m}
eq0\). The acceleration is in the opposite direction of the velocity (because drag force opposes the motion), so the horizontal velocity is decreasing.

Step2: Analyze vertical direction

In the vertical direction, \(F_{net - y}=mg - F_{lift}\) (where \(mg\) is the weight and \(F_{lift}\) is the lift force). Given \(F_{lift}0\) and \(a_{y}=\frac{mg - F_{lift}}{m}>0\) (direction is downward). According to \(v = v_{0}+a_{y}t\), since \(a_{y}>0\), the vertical velocity (downward - direction) is increasing.

Answer:

D. Decreasing, Increasing downward