Round to the nearest tenth unless indicated otherwise.
-Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity v. If a car traveling at a speed of $50 \mathrm { mph }$ with a surface area of $36 \mathrm { ft } ^ { 2 }$ experiences a drag of $270 \mathrm {~N}$ (Newtons), how fast must a car with $35 \mathrm { ft } ^ { 2 }$ of surface area travel in order to experience a drag force of $231 \mathrm {~N}$ ?
A) $49 \mathrm { mph }$
B) $46 \mathrm { mph }$
C) $41 \mathrm { mph }$
D) $44 \mathrm { mph }$

Question

Quizplus · Accepted Answer

The drag force formula can be expressed as $D = kAv^2$, where $D$ is the drag force, $A$ is the surface area, $v$ is the velocity, and $k$ is a constant. Given that a car with a surface area of $36 \mathrm{ft}^2$ and velocity of $50 \mathrm{mph}$ experiences a drag of $270 \mathrm{N}$, we can find the constant $k$ and then use it to find the required velocity for a car with a surface area of $35 \mathrm{ft}^2$ to experience a drag of $231 \mathrm{N}$. The calculation involves setting up a proportion based on the given and required conditions and solving for the unknown velocity. The correct answer, after performing the calculations and rounding to the nearest tenth, is $44 \mathrm{mph}$.

Round to the Nearest Tenth Unless Indicated Otherwise 50mph50 \mathrm { mph }50mph

Round to the Nearest Tenth Unless Indicated Otherwise $50 \mathrm { mph }$