Question

Hard Calculus question
At noon, ship A is 45km due south of Ship B. Ship A sails north at 10kmph and ship B sails east at 7.5kmph. At what time are they closest?

Answer 1

at time t the ship is (45-10t ) km due south but ship b is 7.5 km east so
distace(d)=sqrt((45-10t)^2+(7.5t)^2)
when distace is smallest then \[d^2=(45-10t)^2+(7.5t)^2\]is smallest
let D=d^2=(45)^2-900t+(100+7.5^2)t^2
\[\frac{dD}{dt}=-900+2(100+7.5^2)t=0\]gives t=2.88
putting t=2.88 you get d= 27Km

Answer 2

i think u got it...