An off-roader explores the open desert in her Hummer. First she drives 25 ∘ west of...
An off-roader explores the open desert in her Hummer. First she drives 25 ∘ west of north with a speed of 7.0 km/h for 15 minutes, then due east with a speed of 13 km/h for 7.5 minutes. She completes the final leg of her trip in 22 minutes.
What is the direction and speed of travel on the final leg? (Assume her speed is constant on each leg, and that she returns to her starting point at the end of the final leg.)
What is v in km/h?
Homework Answers
Speed in first leg=7 km/h
Time=7.5 minutes
Distnace travelled in first leg=7*15/60=1.75 km
Speed in second leg=13 km/h
Time in secomd leg=7.5 minutes
Distance travelled in second leg=13*7.5/60=1.625 km
Total horizontal distance=-1.75*sin25+1.625=0.885 km
Total vertical distance=1.75*cos25=1.59 km
Distance from.origin=sqrt(0.885²+1.59²)=1.82 km
Time taken for last leg=22 minutes
Speed in last leg=1.82/(22/60)=4.95 km/hr
Direction in which it will travel=arctan(0.885/1.59)=29.1° south of west
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