Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity $\mathrm{v}$. If a car traveling at a speed of $60 \mathrm{mph}$ with a surface area of $31 \mathrm{ft}^{2}$ experiences a drag of $316.2 \mathrm{~N}$ (Newtons), how fast must a car with $36 \mathrm{ft}^{2}$ of surface area travel in order to experience a drag force of $330.48 \mathrm{~N}$ ?
A) $51 \mathrm{mph}$
B) $54 \mathrm{mph}$
C) $56 \mathrm{mph}$
D) $59 \mathrm{mph}$

Question

Quizplus · Accepted Answer

The drag force $D$ varies jointly with the surface area $A$ and the velocity $v$, so we can write $D = kAv$, where $k$ is a constant of proportionality. Given $D_1 = 316.2$ N for $A_1 = 31 \mathrm{ft}^2$ and $v_1 = 60 \mathrm{mph}$, we can find $k$ by rearranging the formula to $k = D_1 / (A_1v_1)$. To find the velocity $v_2$ for $A_2 = 36 \mathrm{ft}^2$ and $D_2 = 330.48$ N, we use the same formula with the known $k$, solving for $v_2$. The calculation shows that the required velocity is approximately $54 \mathrm{mph}$.

Wind Resistance or Atmospheric Drag Tends to Slow Down Moving v\mathrm{v}v

Wind Resistance or Atmospheric Drag Tends to Slow Down Moving $\mathrm{v}$