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cmflores3245
25.09.2019 •
Mathematics
Two cars, car x and car y , start moving from the same point p on a cross intersection. car x is travelling east and car y is travelling north. some time later car x is 60 km east of point p and travelling in an easterly direction at 80 km/h and car y is 80 km north of point p and travelling in a northerly direction at 100 km/h. how fast is the distance between car x and car y changing?
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Ответ:
let the distance traveled by car Y by y km
their paths form a right-angled triangle.
Let the distance between them be D km
D^2 = x^2 + y^2
2D dD/dt = 2x dx/dt + 2y dy/dt
dD/dt = (x dx/dt + y dy/dt)/D
at the given case:
x = 60, y = 80 , dx/dt = 80, dy/dt = 100
D^2 = 60^2 + 80^2 = 10000
D = 100
dD/dt = (60(80) + 80(100))/100
= 128
Ответ: