Related Rates of Planes: Calculating Distance Change at Noon

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SUMMARY

The discussion focuses on calculating the rate of change of distance between two planes at noon, with one traveling east at 100 km/hr and the other south at 200 km/hr. At noon, the distance between the planes is increasing at a rate of 100 km/hr, while at 11 am, the rate is 0 km/hr, and at 1 pm, it is approximately 158.1 km/hr. By 2 pm, the rate reaches about 186.1 km/hr. The calculations involve using the relationship between the distances and speeds of the planes, confirming that the initial speeds provided are relatively low for typical aircraft.

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shanshan
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Homework Statement


At ten am, a plane traveling east at 100km/hr is 500 km west of a jet traveling south at 200km/hr. At what rate is the distance between them changing at noon?


Homework Equations





The Attempt at a Solution


2aa' + 2bb' = 2cc'
2(300)(-100) + 2(400)(200) = (1000)c'
-60000 + 160000 = 1000c'
c' = 1000 km/h

i need 186.1 km/h though.
 
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At noon, I find that the planes are moving apart at a rate of 100 km/hr at noon. I checked a couple of other times to see the rate at which the planes are moving apart. At 11am, the rate of change of distance was 0 km/hr. at 1pm, the rate of change of distance was about 158.1 km/hr. At 2pm, the rate of change is about 186.1 km/hr.

Are you sure you've given us the right times?

BTW, these are a couple of very slow planes. Many planes stall at speeds of 100km/hr, and a speed of 200km/hr for a jet is likewise very slow.
 
yes, these are the times listed on my sheet. there may be a typo though.
 

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