Ambiguous Problem Statement on Determining Speed of Aircraft

[vcsharp2003]

Homework Statement

An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is
30 degrees. What is the speed of the aircraft?

Relevant Equations

s=vt, where s is the distance travelled at a speed of v in time t

When I attempted this problem, I came up with two different solutions and answers, and both seem correct to me. However, the answer obtained by the first method is correct according to the book.

The methods I used are as in screenshots below.

Isn't the problem statement ambiguous, or maybe I am missing something?

In diagrams below, point $G$ is the observation point on the ground, $P_1$ is the initial observed position of the aircraft and $P_2$ is the final observed position of the aircraft.

 

[hmmm27]

The relative position of the observer isn't given, so you're right. Note that there's more possibiliites, if you don't assume the aircraft's path is directly overhead the observer.

 

[vcsharp2003]

The relative position of the observer isn't given, so you're right. Note that there's more possibiliites, if you don't assume the aircraft's path is directly overhead the observer.

By more possibilites, you mean the situation where the vertical line from $G$ going up does not intersect the line $P_1P_2$, but intersects the extended line from $P_1P_2$.

 

[hmmm27]

By more possibilites, you mean the situation where the vertical line from $G$ going up does not intersect the line $P_1P_2$, but it intersects the extended line from $P_1P_2$.

As well as the two most reasonable possibilities - the observer's position being directly under the aircraft's path at either the start(/finish) or midpoint of the observation - it could well be 100 miles away.

 

[vcsharp2003]

As well as the two most reasonable possibilities - the observer's position being directly under the aircraft's path at either the start(/finish) or midpoint of the observation - it could well be 100 miles away.

I am curious whether there is a Physics book for high school students that is known for having an accurate list of questions/problems, and not ambiguous questions/problems. Maybe there is no such book in the whole world.

Ambiguous questions/problems discourages a student from studying Physics.

 

[hmmm27]

If there was, we wouldn't hear about it

 

[vcsharp2003]

If there was, we wouldn't hear about it

It's sad that no one in this world can come up with an accurate list of questions/problems in high school Physics.

 

[256bits]

By more possibilites, you mean the situation where the vertical line from $G$ going up does not intersect the line $P_1P_2$, but intersects the extended line from $P_1P_2$.

Indeed. In addition, the problem does not state the vertical intersects the pathline of the aircraft.

 

[jbriggs444]

Indeed. In addition, the problem does not state the vertical intersects the pathline of the aircraft.

Or even that the craft is flying in a straight line.

 

[jbriggs444]

It's sad that no one in this world can come up with an accurate list of questions/problems in high school Physics.

But not surprising. Unambiguous problems are a dime a dozen. There are lots of them. We tend not to notice them. It is the ambiguous or otherwise bad ones that you remember and complain about.

Since complaints about textbooks produce no useful relief for the complainer, we develop coping strategies. Strategies that may be useful in the real world where the problems with problems get much worse. [In the real world, they don't give you the information you need. The information they do give you may be incorrect. The problem they give you may not be the problem you need to solve. And a solution may not even exist].