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"#
#v_a=22.06 " "mph#

enter image source here

#bar (AD)=50* 10/60=50/6=8.33 " miles"#

#bar(DE)=62*5/60=31/6=5.17" miles"#

#bar(EB)=26*6/60=156/60=2.6 " miles"#

#bar(AD)=bar(EC)#
#bar(DE)=bar(AC)#

#"use ABC triangle"#

#bar(AC)=bar(DE)=5.17#

#bar(BC)=bar(EC)-bar(EB)#

#bar(BC)=8.33-2.6=5.73#

#"displacement"=bar(AB)=sqrt(bar(AC)^2+bar(BC)^2)#

#bar(AB)=sqrt((5.17)^2+(5.73)^2)#

#bar(AB)=7.72" miles"#

#"average velocity is described as " v_a=("displacement")/("time elapsed")#

#"time elapsed="10/60+5/60+6/60=21/60=0.35 " "h#

#v_a=(bar(AB))/(0.35)#

#v_a=(7.72)/(0.35)#

#v_a=22.06 " "mph#