Posted by **Fizza** on Wednesday, September 28, 2011 at 2:30pm.

A plane has an airspeed of 200 {mph}. The pilot wishes to reach a destination 600 {mi} due east, but a wind is blowing at 50 {mph} in the direction 30 degrees north of east.

a)In what direction must the pilot head the plane in order to reach her destination? answer in south of east

b)How long will the trip take?

answer in hours

can you please show me step by step so i can check my answer?

thanks

- Physics-ASAP -
**Steve**, Wednesday, September 28, 2011 at 3:57pm
You want two vectors which add up to (0,600). The airspeed has length 200t in an unknown direction, angle a. The other has length 50t, in the direction 30º north of east.

So, if the destination D = (600,0)

P is the point where the plane would have ended up with no crosswind.

P = (x,y) where

y = -25t because of the 30º angle.

So, now we have two right triangles.

On the left, the hypotenuse = 200t, height = 25t, base = 25t√63

On the right, hypotenuse=50t, height=25t, base=25t√3

Now, we know that the two bases add up to 600mi.

25t(√63+√3) = 600

t = 2.48 hrs

Using the plane's triangle, sin(a) = 1/8

a = 7.18º south of east.

You can use the law of cosines to verify that the numbers are correct.

## Answer This Question

## Related Questions

- Physics - a plane has an airspeed of 200 mph. the pilot wants to reach a ...
- Physics - A plane is heading due south with an airspeed of 211 mph. A wind from ...
- pre-cal - a pilot wants to fly on a bearing of 66.4 degrees. by flying due east...
- Pre calculus - A plane is headed due south with an airspeed of 190 mph. A wind ...
- calculus iii - What heading (or direction) and airspeed (speed in still air) are...
- calculus III - What heading (or direction) and airspeed (speed in still air) are...
- Physics - An airplane ﬂies at airspeed (relative to the air) of 430 km/h...
- Physics - A light plane attains an airspeed of 491 km/h. The pilot sets out for ...
- word problem - An airplane is flying with a heading of 60 degrees east of north ...
- physics - The pilot of an airplane wishes to fly due north, but there is a 71 km...

More Related Questions