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yawa3891 [41]
4 years ago
7

Two straight roads diverge at an angle of 45°. Two cars leave the intersection at 2:00 P.M., one traveling at 32 mi/h and the ot

her at 54 mi/h. How far apart are the cars at 2:30 P.M.? (Round your answer to two decimal places.)
Physics
1 answer:
svp [43]4 years ago
3 0

Answer:19.34 miles

Explanation:

Given

First car travels with 32 mi/h

second travels with 54 mi/h

they leave at 2:00 Pm at 45

distance traveled by them is 0.5 hr

suppose First is traveling towards x axis and another travels 45 to it

Distance traveled by first car is 32\times 0.5=16 miles

Position vector of first car after 0.5 hr

\vec{r_1}=32\times 0.5(\cos (45)\hat{i})

Position vector of second car after 0.5 hr

\vec{r_2}=54\times 0.5(\cos (45)\hat{i}+\sin (45)\hat{j})

distance between them

\vec{r_{21}}=27(\cos (45)\hat{i}+\sin (45)\hat{j})-16(\cos (45)\hat{i})

\vec{r_{21}}=3.09\hat{i}+27\hat{j}\sin (45)

distance between them|\vec{r_{21}}|=19.34

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