Question

police use the function $v(l) = \sqrt{20l}$ 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. round your answers to the nearest tenth as needed

a) at the scene of an accident, a police officer measures a car’s skid marks to be 109 feet long. approximately how fast was the car traveling?
the car was traveling at approximately \boxed{} miles per hour

b) one of the people involved in the accident says that he was traveling 55 mph when he braked. how long in feet should his car’s skid marks be?
the skid marks should be approximately \boxed{} feet long.

Explanation:

Step1: Solve part (a)

We are given the function \( V(L)=\sqrt{20L} \) and \( L = 109 \) feet. Substitute \( L = 109 \) into the function:
\( V(109)=\sqrt{20\times109} \)
First, calculate \( 20\times109 = 2180 \). Then, find the square root of 2180: \( \sqrt{2180}\approx46.7 \) (rounded to the nearest tenth).

Step2: Solve part (b)

We are given \( V = 55 \) mph. Use the function \( V(L)=\sqrt{20L} \), so we set up the equation \( 55=\sqrt{20L} \).
Square both sides to eliminate the square root: \( 55^{2}=20L \)
Calculate \( 55^{2}=3025 \). Then, solve for \( L \): \( L=\frac{3025}{20}=151.25 \)

Answer:

a) The car was traveling at approximately \( \boldsymbol{46.7} \) miles per hour.
b) The skid marks should be approximately \( \boldsymbol{151.25} \) feet long.