Pilot disobeys physics and faces consequences

Classical Mechanics Level 3

An airplane wants to fly from $A$ to city $B$ which is $1000 \text{ km}$ due north of city $A$ . The speed of the plane in still air is $500\text{ km/hr}$ . The pilot neglects the effect of the wind and directs his plane due north and two hours later find himself $300\text{ km}$ due north-east of city $B$ . The magnitude of wind velocity is (in $\text{ km/hr}$ ) .

Try my set .

The answer is 150.

2 solutions

Tanishq Varshney
Apr 25, 2015

Suppose plane reaches point $P$ .

From $(1)$ and $(2)$

$300cos45^{o} \hat { i } +(1000+300cos45^{o}) \hat { j } =2x \hat { i } +(1000+2y) \hat { j }$

Comparing $\hat { i }$ and $\hat { j }$

$x=\frac{150}{\sqrt{2}}$ and $y=\frac{150}{\sqrt{2}}$

velocity of wind $v_{w}=\frac{150}{\sqrt{2}} \hat { i } +\frac{150}{\sqrt{2}} \hat { j }$

$|v_{w}|=\sqrt{x^2+y^2}$

$|v_{w}|=150~km/hr$

Cheers!!

Peter Macgregor
Apr 27, 2015

Neglecting the wind, the plane would normally fly from A to B in two hours.

The effect of the wind has been to blow the plane off course by 300km. Since the journey took 2 hours, the wind must have a speed of 150 km/h.

That would only be true if wind was 150kmh due north but he didnt travel 1300 miles. His distnac was about 1230.55 miles since his path was north north east approx imately.

Greg Grapsas - 1 year, 10 months ago

I too used this straight forward easiest solution.

Niranjan Khanderia - 6 years, 1 month ago

Pilot disobeys physics and faces consequences

Try my set .

The answer is 150.

2 solutions

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