How can the pilot reach his original destination after encountering bad weather?

In summary, the pilot flew 40 miles west to find an airport, then 20 miles at 15° east of south to find the third airport. He then flew northeast to his original destination.
  • #1
JJ91284
7
0

Homework Statement



The pilot of a small plane finds that the airport where he intended to land is fogged in. He flies 40 miles west to another airport to find that conditions there are too icy for him to land. He flies 20 miles at 15° east of south and is finally able to land at the third airport.

Questions

How far and in what direction must he fly the next day to go directly to his original destination

So the 40 miles would be the hypotenuse where the 20 miles would be the adjacent angle. Those to intersect at 75 degrees (inside angle). I also know that he has to fly NE to get to his original destination.

So I took 40 sin 75= 38.63 which apparently is wrong because I just got zero points for that online homework question.

I need to figure out the answer before I can move on to the rest of the problems.

Any real help would be appreciated. Please let me know what you did as well.

That answere should allow me to answer this part.

How many extra miles beyond his original flight plan has he flown?

Thanks for the help
 
Physics news on Phys.org
  • #2
Try setting up a coordinate system with the original airport at the origin and the axes as N, E, S, and W.
 
  • #3
Welcome to PF!

Hi JJ91284! Welcome to PF! :smile:
JJ91284 said:
… So the 40 miles would be the hypotenuse where the 20 miles would be the adjacent angle. Those to intersect at 75 degrees (inside angle). I also know that he has to fly NE to get to his original destination.

So I took 40 sin 75= 38.63 which apparently is wrong because I just got zero points for that online homework question.

No, you're assuming that the angle at the third airport is 90º … it isn't!

You know two sides and their enclosed angle …

so if you know the cosine rule for triangles, use it …

otherwise, as chrisk :smile: suggests, use coordinates. :wink:
 
  • #4
I looked up the law of cos which states C^2=a^2+b^2-2ab cos (c)

So I plugged in my numbers and I got 39.82. Would someone mind just checking my solution and seeing if it works
 
  • #5
Ok well I know my unknown side is 39.82. My last question where it asks how much extra did the plane fly comes out to 99.82 miles.

Now the question asks

I figure out the unknown side which is 39.82 viat the law of cos. I looked that up via the internet, I'd forgotten that rule. I also used the law of sin to get the angles.

How far and in what direction must he fly the next day to go directly to his original destination?
39.82 mi at ?? north of east

I entered 76 (I did that or 74, I forgot which) degrees north of east and it came back wrong. The only other measure I can think of would be 29 degrees. Is that 29 correct?
 
  • #6
Hi JJ91284! :smile:

Yes, 39.82 is correct. :smile:

It would help both us and you if you wrote out your full calculations …

in this case, if you write it out, you'll see that you've correctly calculated the wrong angle!

Useful tip: always give the points of your triangle letters, so you can write equations like sinA/CAB = sinB/ABC, and be less likely to make mistakes.

So … maybe it is 29, and maybe it isn't …

what do you think? :wink:
 

FAQ: How can the pilot reach his original destination after encountering bad weather?

1. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of both speed and direction. In other words, velocity takes into account the direction an object is moving in addition to its speed.

2. How do I calculate acceleration?

Acceleration is calculated by dividing the change in an object's velocity by the time it took for that change to occur. The formula for acceleration is: a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What is Newton's first law of motion?

Newton's first law of motion, also known as the law of inertia, states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. In other words, objects resist changes in their motion.

4. What is the relationship between force and motion?

Force and motion are directly related. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be.

5. How does gravity affect objects?

Gravity is the force that attracts objects with mass towards each other. The strength of gravity between two objects depends on their mass and the distance between them. The greater the mass of an object, the stronger its gravitational pull, and the closer two objects are to each other, the stronger their gravitational attraction will be.

Back
Top