maths help:) (1 Viewer)

mac1996 · Oct 28, 2012

Joel is 700 km north of a town, travelling towards it at an average speed of 75 km/h. Nick is 680 km east of the town, travelling towards it at 80 km/h. Show that after t hours, the distance between Joel and Nick is given by, d= √(952400-213800t +12025t^2)

Sy123 · Oct 28, 2012

Establish the givens:

Call the distance of Joel to the town J, the distance of Nick to the town N.

$\frac{dJ}{dt}=-75 \ \ \ \ \ \frac{dN}{dt}=-80$

Integrate:

$J=-75t+C_1 \\ N=-80t+C_2$

t=0 J=700 N=680

$J=-75t+700 \\ N=-80t+680$

Use pythagoras

$N^2+J^2=d^2 \\ \\ d= \sqrt{(-75t+700)^2+(-80t+680)^2}=$Answer$$

maths help:) (1 Viewer)

mac1996

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Sy123

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