In a fit of pique, the Canadians fire a cannonball due south from vancouver (lat 49.2 degrees N) at a randomly picked city (39.4 degrees N). Assuming the cannonball takes 48 minutes to get there, by how far and in what direction will the cannonball miss?
LOL - this is the other side of the hurricane.
Do this the same way but this time you really do have to use my east speed = 21600*cosine of latitude to get the speeds east at 49.2 and 39.4
Do it just as we did the last problem, except you will end up west this time because you are moving south.
and of course instead of an easy 1/2 hour we now have 48/60 hours
East speed at 49.2 = 21600 * cos 49.2 nm/ 24hr
You take it from there.
By the way you may have a more accurate circumference of earth than my 360 degrees times 60 nm/degree at the equator. I do not have any books here.
To determine the distance and direction by which the cannonball misses the target city, we can use some basic trigonometry and geographic coordinates. Here's how you can calculate it:
1. Identify the geographic coordinates of the two locations:
- Vancouver: Latitude = 49.2 degrees N
- Target city: Latitude = 39.4 degrees N
(We'll assume the longitude coordinates are the same for simplicity.)
2. Calculate the difference in latitude:
- Δlat = Target latitude - Vancouver latitude
Δlat = 39.4 - 49.2 = -9.8 degrees
3. Convert the latitude difference from degrees to kilometers:
- 1 degree of latitude is approximately 111 km.
- Distance (latitude) = Δlat * 111 km
Distance (latitude) = -9.8 * 111 = -1087.8 km
(Negative value indicates the target city is to the south of Vancouver.)
4. Calculate the distance traveled by the cannonball:
- Given the time of flight as 48 minutes, we need to determine the speed.
- Assuming the cannonball traveled in a straight line, we convert the time to hours: 48 minutes = 0.8 hours.
- Distance (travel) = Speed * Time
We don't have the speed, so we can't determine the actual distance traveled. However, we can still determine the latitudinal distance by making an estimation.
5. Estimate the distance traveled by the cannonball:
- Assuming the average speed of the cannonball is constant, we can approximate it based on the latitude difference and the time of flight.
- Average Speed = Distance (latitude) / Time
Average Speed = -1087.8 km / 0.8 hours = -1359.75 km/h (approx.)
6. Calculate the distance missed by the cannonball:
- We know the speed, and we know the time it took to reach the target city, so now we can calculate the distance missed.
- Distance (missed) = Speed * Time
Distance (missed) = -1359.75 km/h * 0.8 hours = -1087.8 km
(Negative value indicates the cannonball fell short, missing the target to the south of it.)
7. Determine the direction by which the cannonball missed:
- Since the cannonball was fired due south, it missed toward the south direction.
Therefore, the cannonball misses the target city by approximately 1087.8 kilometers to the south (negative latitude direction).