A car drives north at 50 mi/h for 10 min and then turns east and goes 5.0 min at 62 mi/h. Finally, it goes southwest at 26 mi/h for 6.0 min. what is the car's displacement? What is its average velocity for this trip?

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A car drives north at 50 mi/h for 10 min and then turns east and goes 5.0 min at 62 mi/h. Finally, it goes southwest at 26 mi/h for 6.0 min. what is the car's displacement? What is its average velocity for this trip?

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Answer 1 · 2016-09-28T12:46:04

$please have a look the animation$ $"please have a look the animation"$
$v_{a} = 22.06 m p h$ $v_a=22.06 " "mph$

Explanation:

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$¯ ¯¯¯¯ ¯ A D = 50 \cdot \frac{10}{60} = \frac{50}{6} = 8.33 miles$ $bar (AD)=50* 10/60=50/6=8.33 " miles"$

$¯ ¯¯¯¯ ¯ D E = 62 \cdot \frac{5}{60} = \frac{31}{6} = 5.17 miles$ $bar(DE)=62*5/60=31/6=5.17" miles"$

$¯ ¯¯¯¯ ¯ E B = 26 \cdot \frac{6}{60} = \frac{156}{60} = 2.6 miles$ $bar(EB)=26*6/60=156/60=2.6 " miles"$

$¯ ¯¯¯¯ ¯ A D = ¯ ¯¯¯¯ ¯ E C$ $bar(AD)=bar(EC)$
$¯ ¯¯¯¯ ¯ D E = ¯ ¯¯¯¯ ¯ A C$ $bar(DE)=bar(AC)$

$use ABC triangle$ $"use ABC triangle"$

$¯ ¯¯¯¯ ¯ A C = ¯ ¯¯¯¯ ¯ D E = 5.17$ $bar(AC)=bar(DE)=5.17$

$¯ ¯¯¯¯ ¯ B C = ¯ ¯¯¯¯ ¯ E C - ¯ ¯¯¯¯ ¯ E B$ $bar(BC)=bar(EC)-bar(EB)$

$¯ ¯¯¯¯ ¯ B C = 8.33 - 2.6 = 5.73$ $bar(BC)=8.33-2.6=5.73$

$displacement = ¯ ¯¯¯¯ ¯ A B = \sqrt{{¯ ¯¯¯¯ ¯ A C}^{2} + {¯ ¯¯¯¯ ¯ B C}^{2}}$ $"displacement"=bar(AB)=sqrt(bar(AC)^2+bar(BC)^2)$

$¯ ¯¯¯¯ ¯ A B = \sqrt{{(5.17)}^{2} + {(5.73)}^{2}}$ $bar(AB)=sqrt((5.17)^2+(5.73)^2)$

$¯ ¯¯¯¯ ¯ A B = 7.72 miles$ $bar(AB)=7.72" miles"$

$average velocity is described as v_{a} = \frac{displacement}{time elapsed}$ $"average velocity is described as " v_a=("displacement")/("time elapsed")$

$time elapsed= \frac{10}{60} + \frac{5}{60} + \frac{6}{60} = \frac{21}{60} = 0.35 h$ $"time elapsed="10/60+5/60+6/60=21/60=0.35 " "h$

$v_{a} = \frac{¯ ¯¯¯¯ ¯ A B}{0.35}$ $v_a=(bar(AB))/(0.35)$

$v_{a} = \frac{7.72}{0.35}$ $v_a=(7.72)/(0.35)$

$v_{a} = 22.06 m p h$ $v_a=22.06 " "mph$

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A car drives north at 50 mi/h for 10 min and then turns east and goes 5.0 min at 62 mi/h. Finally, it goes southwest at 26 mi/h for 6.0 min. what is the car's displacement? What is its average velocity for this trip?

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