Answer
$1600$ feet.
Work Step by Step
Step 1:- Translate the statement to form a equation.
Let the distance be $D$.
and the time be $T$.
Because $D$ varies directly as $T^2$ we have:
$\Rightarrow D=kT^2$ ...... (1)
Step 2:- Substitute the first set of values into equation (1) to find the value of $k$.
The given values are $D=144$ feet and $T=3$ seconds.
Substitute into the equation (1).
$\Rightarrow 144=k(3)^2$
$\Rightarrow 144=9k$
Divide both sides by $9$.
$\Rightarrow \frac{144}{9}=\frac{9k}{9}$
Simplify.
$\Rightarrow 16=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=16$ into the equation (1).
$\Rightarrow D=16T^2$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $T=10$ seconds into the equation (2).
$\Rightarrow D=16(10)^2$
Simplify.
$\Rightarrow D=1600$
Hence, the distance that a body falls from rest in $10$ seconds is $\$1600$ feet.
