Question

question 24
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 127 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 56 mph when he braked. how long in feet should his cars skid marks be? round the length to the nearest tenth.

$\text{ft}$
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question 25
find the length of the hypotenuse of the right triangle pictured below.
12
9
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Explanation:

Step1: Solve part a

Given the formula $V(L)=\sqrt{20L}$, and $L = 127$. Substitute $L$ into the formula.
$V(127)=\sqrt{20\times127}=\sqrt{2540}\approx50.4$

Step2: Solve part b

Given $V(L) = 56$ and $V(L)=\sqrt{20L}$. Set up the equation $\sqrt{20L}=56$. Square both sides to get $20L = 56^{2}=3136$. Then solve for $L$: $L=\frac{3136}{20}=156.8$

Step3: Solve for hypotenuse of right - triangle

Use the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 9$ and $b = 12$. So $c=\sqrt{9^{2}+12^{2}}=\sqrt{81 + 144}=\sqrt{225}=15$

Answer:

a) $50.4$ mph
b) $156.8$ ft
c) $15$