Question

The pressure $P$ of wind on a sail varies jointly as the area $A$ of the sail and the square of the velocity $V$ of the wind. The pressure on a square foot is $1$ pound when the velocity is $16$ miles per hour. The velocity of the wind when the pressure on a square yard is $36$ pounds is:

$10\dfrac23$ mph

$96$ mph

$32$ mph

$1\dfrac13$ mph

$16$ mph

Answer: C

Concepts:ratio and proportion unit conversion

Difficulty rating: 1520

Small Hint:

Use $P=kAV^2$ and remember that one square yard is nine square feet

Big Hint:

The first condition gives $1=k(1)(16^2)$

Solution:

Write $P=kAV^2.$ From $1=k(1)(16^2),$ we get $k=\frac{1}{256}.$ A square yard has area $9$ square feet, so $36=\frac1{256}\cdot9V^2.$ Thus $V^2=1024$ and the positive speed is $V=32$ mph.

Thus, the correct answer is C.

1951 AMC 12 Problem 28

Answer: C

Difficulty rating: 1520

Small Hint:

Big Hint:

Solution:

Problem 28 in Other Years