a. We can use trigonometry to find the distance between M3 and M7. Let's call this distance "x". We know that M7 has traveled 18 meters in 30 minutes, which means its speed is:
18 meters / 30 minutes = 0.6 meters per minute
We also know that M7 and M3 are forming a right angle (M7 is heading on a bearing of 277 degrees, which is 13 degrees from due south). So we can use the tangent function to find x:
tan(13) = x / 0.6
x = 0.6 * tan(13) ≈ 0.13 km
Therefore, M3 is about 0.13 kilometers away from M7.
b. Since M3 has been heading due West for 30 minutes, we can find the distance it has traveled by multiplying its speed by the time:
distance = speed * time
We don't know M3's exact speed, but we do know that it has been traveling in a straight line. So we can use the Pythagorean theorem to find the distance it has traveled:
distance = √(x^2 + (18/60)^2)
where x is the distance we found in part (a), and 18/60 is the distance that M7 has traveled (since speed = distance / time, and M7 has traveled for 30 minutes).
Plugging in the numbers, we get:
distance = √(0.13^2 + 0.005^2) ≈ 0.13 km
Therefore, M3 has traveled about 0.13 kilometers.
Two patrol boats M3 and M7 leave port at the same port at the same time. M3 heads due West and M7 on the bearing 277 degrees. After 30 minutes M7 has travelled 18 meters and observe M3 in the direction due south.
a. How far is M3 from M7?
b. How far has M3 travelled?
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