Question

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 other at 54 mi/h. How far apart are the cars at 2:30 P.M.? (Round your answer to two decimal places.)

Answer 1

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$|\vec{r_{21}}|=19.34$