Problems with Problems

Math Power 11 page 512, question 37

A satellite is in an orbit 1000 km above the surface of the Earth. A receiving dish is located so that the directions from the satellite to the dish and from the satellite to the centre of the Earth make an angle of 27º. If a signal from the satellite travels at 3 x 10^8 m/s, how long does it take to reach the dish, to the nearest thousandth of a second? Assume that the radius of the Earth is 6370 km.

In analyzing the above question it seems to be a reasonably good question. It has good and memorable imagery of a satellite orbiting the Earth, along with a nice diagram, not shown here. This imagery is not necessarily the most practical, but it does the job and is not too distracting for the most part, as the question is not about the satellite orbiting. That being said the wording of the problem is not as clear or concise as it could be. In the question we are given all the information required to solve the problem but it is given awkwardly. If it were not for the diagram it may become somewhat unclear as to what the set up should look like. The question gives the angle made by the dish, the satellite and the centre of the Earth in a confusing way, instead it could just read something like, "When the satellite makes an angle of 27º with the receiving dish and the centre of the Earth it sends a signal to the dish." This would be a better way to give the necessary information and the reader wouldn't become confused about "the directions" and also, on a more literal note, the question states that the satellite is orbiting, implying that it is moving and thus the angle would be changing with time, some students could be very distracted by this inaccuracy.