Question

question 21
police use the formula $v(l)=sqrt{20l}$ to estimate the speed of a car in miles per hour, based on the length, $l$, in feet, of its skid marks when suddenly braking on a dry, asphalt road.
a) at the scene of an accident, a police officer measures a cars skid marks to be 215 feet long. approximately how fast was the car traveling? round the speed to the nearest tenth.
$\text{mph}$
b) one of the people involved in the accident says that he was traveling 51 mph when he braked. how long in feet should his cars skid marks be? round the length to the nearest tenth.
$\text{ft}$

Explanation:

Step1: Substitute $L = 215$ into formula

Given $V(L)=\sqrt{20L}$, substitute $L = 215$. So $V(215)=\sqrt{20\times215}=\sqrt{4300}$.

Step2: Calculate the value

$\sqrt{4300}\approx65.6$ mph.

Step3: Solve for $L$ when $V = 51$

Set $V(L)=\sqrt{20L}=51$. Square both sides: $20L = 51^{2}=2601$.

Step4: Calculate $L$

$L=\frac{2601}{20}=130.05\approx130.1$ ft.

Answer:

a) $65.6$ mph
b) $130.1$ ft