Aplane flying horizontally at an altitude of 1 mile and a speed of of 500mih passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it is 2mi away from the station.

447.2 mph

Explanation:

The vertical distance from the plane to the station is 1 mile.

The horizontal distance from the plane to the station is x miles.

The distance between the plane and station is therefore:

d² = 1² + x²

Taking derivative with respect to time:

2d dd/dt = 0 + 2x dx/dt

d dd/dt = x dx/dt

We know that x = 2 miles and dx/dt = 500 mi/hr.  We need to find d when x=2.

d² = 1² + 2²

d² = 5

d = √5

Therefore:

√5 dd/dt = (2) (500)

dd/dt = 1000/√5

dd/dt = 200√5

dd/dt ≈ 447.2 mph

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min