The eye of a hurricane passes over Grand
Bahama Island. It is moving in a direction
77.2
◦ north of west with a speed of 49.0 km/h.
Exactly 2.92 hours later, the course of the
hurricane shifts due north, and its speed slows
to 22.4 km/h, as shown.
How far from Grand Bahama is the hurricane
4.64 h after it passes over the island?
Answer in units of km
you have two sides (speed * time) and the included angle.
So, use the law of cosines.
To find the distance from Grand Bahama Island to the hurricane 4.64 hours after it passes over the island, we need to break down the problem into two parts:
1. Find the distance the hurricane travels in the first 2.92 hours.
2. Find the distance the hurricane travels in the next 1.72 hours.
Let's start with the first part:
1. Find the distance the hurricane travels in the first 2.92 hours.
The hurricane's speed is given as 49.0 km/h, and it is moving in a direction 77.2 degrees north of west. To find the distance it travels, we can use the formula:
distance = speed × time
distance1 = 49.0 km/h × 2.92 h
Now, let's calculate the distance1:
distance1 = 49.0 km/h × 2.92 h = 143.08 km
So, the hurricane travels a distance of 143.08 km in the first 2.92 hours.
Now, let's move on to the second part:
2. Find the distance the hurricane travels in the next 1.72 hours.
The hurricane's speed has now slowed down to 22.4 km/h, and it is moving due north (north direction). To find the distance it travels, we can again use the formula:
distance = speed × time
distance2 = 22.4 km/h × 1.72 h
Now, let's calculate the distance2:
distance2 = 22.4 km/h × 1.72 h = 38.528 km
So, the hurricane travels a distance of 38.528 km in the next 1.72 hours.
Finally, to find the total distance from Grand Bahama Island to the hurricane 4.64 hours after it passes over the island, we add the distances from the two parts:
total distance = distance1 + distance2
total distance = 143.08 km + 38.528 km
Now, let's calculate the total distance:
total distance = 181.608 km
Therefore, the hurricane is approximately 181.608 km away from Grand Bahama Island 4.64 hours after it passes over the island.