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Car A is traveling north on a straight highway and car B is traveling west on a different straight highway. Each car is approaching the inte
Question
Car A is traveling north on a straight highway and car B is traveling west on a different straight highway. Each car is approaching the intersection of these highways. At a certain moment, car A is 0.3 km from the intersection and traveling at 95 km/h while car B is 0.4 km from the intersection and traveling at 90 km/h. How fast is the distance between the cars changing at that moment? km/h
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Physics
3 years
2021-08-09T11:21:40+00:00
2021-08-09T11:21:40+00:00 2 Answers
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Answers ( )
Answer:
129 km/hr
Explanation:
Distance of Car A North of the Intersection, y=0.3km
Distance of Car B West of the Intersection, x=0.4 km
The distance z, between A and B is determined by the Pythagoras theorem
Taking derivative of![Rendered by QuickLaTeX.com z^2=x^2+y^2](https://documen.tv/wp-content/ql-cache/quicklatex.com-85d9e73cc1f63b2eb4c2ac297739195c_l3.png)
The distance z, between the cars is changing at a rate of 129 km/hr.
Answer:
The rate at which the distance changes at that moment is 91.743 Km/h
Explanation:
The time for car a to get to the intersection =![Rendered by QuickLaTeX.com \frac{Distance}{Speed}](https://documen.tv/wp-content/ql-cache/quicklatex.com-33afec7b4ade774378bc82e4b68845a2_l3.png)
=![Rendered by QuickLaTeX.com \frac{0.3}{95}](https://documen.tv/wp-content/ql-cache/quicklatex.com-8a7c7461eab75b165d550a782a54509f_l3.png)
= 0.00316 h
The time for car B to get to the intersection =![Rendered by QuickLaTeX.com \frac{Distance}{Speed}](https://documen.tv/wp-content/ql-cache/quicklatex.com-33afec7b4ade774378bc82e4b68845a2_l3.png)
=![Rendered by QuickLaTeX.com \frac{0.4}{90}](https://documen.tv/wp-content/ql-cache/quicklatex.com-393129a1a97d01303d3038f5445c7cc9_l3.png)
= 0.00444 h
Total time =![Rendered by QuickLaTeX.com \sqrt{0.00316^{2} + 0.00444^{2} }](https://documen.tv/wp-content/ql-cache/quicklatex.com-b7f5001f08b465fae388c6cbff48c97c_l3.png)
= 0.00545 h
Total distance between the two cars at that moment =![Rendered by QuickLaTeX.com \sqrt{0.3^{2} + 0.4^{2} }](https://documen.tv/wp-content/ql-cache/quicklatex.com-c66674e4cdf4e1af654415f1fd64cc23_l3.png)
= 0.5 Km
The rate at which the distance between the cars is changing =![Rendered by QuickLaTeX.com \frac{0.5}{0.00545}](https://documen.tv/wp-content/ql-cache/quicklatex.com-cf5cc9b8a0b89b9939e9ab25f6992c35_l3.png)
= 91.743 Km/h