Question

In $\text{case}A,$ when an $80\text{kg}$ skydiver falls with arms and legs fully extended to maximize his surface area, his terminal velocity is $60\text{m/s}.$ In $\text{Case}B,$ when the same skydiver falls with arms and legs pulled in and body angled downward to minimize his surface area, his terminal velocity increases to 80 m/s. In going from $\text{Case A to Case B},$ which of the following statements most accurately describes what the skydiver experiences?

• A. $F_{\text{air resistance}}$ increases and pressure $P$ increases
• B. $F_{\text{air resistance}}$ increases and pressure $P$ decreases
• C. $F_{\text{air resistance}}$ decreases and pressure $P$ increases
• D. $F_{\text{air resistance}}$ remains the same and pressure $P$ increases

Answer 1

The correct option is D $F_{\text{air resistance}}$ remains the same and pressure $P$ increases

For the first part of the question, remember that terminal velocity means the acceleration experienced becomes zero.
Since $a=0{\text{m/s}}^2$, then $\sum F_y=F_{\text{air resistance}}-F_w=0$
$F_{\text{air resistance}}=F_w$
For the second part of the question, while the velocity is higher, the acceleration is still zero. Therefore, the $F_{airresistance}$ is still equal to the skydiver's weight.
$F_{\text{air resistance CaseA}}=F_{\text{air resistance Case B}}$
What has changed is the surface area of the skydiver.
Since pressure is
$P=F/A,$ as $A$ decreases, the pressure experienced increases.
$P_A{A}_A=P_B{A}_B=mg$
Since $A_A>A_B,$ then $P_A<P_B$