Answer
$120\; feet$.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the distance be $D$.
and the speed be $S$.
$\Rightarrow D=kS^2$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $S=45\; miles\; per\; hour$ and $D=67.5\; feet$.
Substitute into the equation (1).
$\Rightarrow 67.5=k(45)^2$
$\Rightarrow 67.5=2025k$
Divide both sides by $2025$.
$\Rightarrow \frac{67.5}{2025}=\frac{2025k}{2025}$
Simplify.
$\Rightarrow \frac{1}{30}=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=\frac{1}{30}$ into the equation (1).
$\Rightarrow D=\frac{1}{30}S^2$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $S=60\; miles\; per\; hour$ into the equation (2).
$\Rightarrow D=\frac{1}{30}(60)^2$
Simplify.
$\Rightarrow D=120$
Hence, the stopping distance is $120\; feet$.
