# Thread: Optimisation QUS, need help plz

1. ## Optimisation QUS, need help plz

Hello. I am having troubles working out this qus. Could you please show me, thanks ^^

1) A motorbike is 30 km directly west of a car and begins moving east at 90km/h. At the same instant, the car begins moving north 60km/h. What will be the minimum distance between the vehicles?

2. Let the car be at the origin. The bike is wwest of the car and heading east, so it's didtance at time t is 30-90t km. The car is heading north at 60, so it's distance at time t is 60t.

The distance between them is ol' Pythagoras:

$(30-90t)^{2}+(60t)^{2}=D^{2}$