A bee flies to a flower 568 m due south of its
hive. The bee’s speed in still air is 0.71 m/s,
and there is a wind blowing toward the south
at 0.19 m/s.
How long will it take the bee to travel to
the flower and back to the hive?
the bee's speed with the wind is 0.71+0.19 = 0.90 m/s
against the wind, it is 0.71-0.19 = 0.52 m/s
time = distance/speed, so the total time for the round trip is
568/0.90 + 568/0.52 = ___ s
Well, if the bee is traveling south and there's a wind blowing towards the south, it's going to be like the bee is trying to walk on a treadmill. Poor little bee! It's going to have to work really hard to get to that flower.
So, let's calculate the bee's relative speed. The bee's speed in still air is 0.71 m/s, and the wind is blowing at 0.19 m/s towards the south. That means the bee's relative speed is 0.71 m/s + 0.19 m/s = 0.9 m/s.
Now, to find how long it will take the bee to travel to the flower and back, we need to divide the total distance by the relative speed. The total distance is 568 m + 568 m = 1136 m. So, the time it will take the bee to travel to the flower and back is 1136 m / 0.9 m/s = 1262.22 seconds.
But wait, I forgot to account for the bee's breaks for tea and nectar! Let's add a couple of minutes for those. So, let's round up to the nearest minute and say it will take the bee approximately 21 minutes to travel to the flower and back to the hive.
Just imagine that little bee, buzzing through the wind, taking breaks for tea and nectar, all in a day's work!
To find the time it will take for the bee to travel to the flower and back to the hive, we need to consider the bee's speed in still air and the effect of the wind.
Step 1: Calculate the speed of the bee with respect to the ground.
- The bee's speed in still air is 0.71 m/s.
- The wind is blowing toward the south at 0.19 m/s.
- Since the bee is flying south, we can subtract the wind speed from the bee's speed in still air to get its speed with respect to the ground: 0.71 m/s - 0.19 m/s = 0.52 m/s.
Step 2: Calculate the time it will take to travel to the flower.
- The distance to the flower is 568 m.
- We can use the formula time = distance / speed to find the time it will take to travel to the flower: time = 568 m / 0.52 m/s = 1092.31 seconds (rounded to two decimal places).
Step 3: Calculate the time it will take to travel back to the hive.
- The distance to travel back to the hive is also 568 m.
- The speed with respect to the ground remains the same at 0.52 m/s.
- Using the same formula, we can find the time it will take to travel back to the hive: time = 568 m / 0.52 m/s = 1092.31 seconds (rounded to two decimal places).
Step 4: Find the total time for the round trip.
- To get the total time for the round trip, we add the time it took to travel to the flower and the time it took to travel back to the hive: 1092.31 seconds + 1092.31 seconds = 2184.62 seconds (rounded to two decimal places).
Therefore, it will take the bee approximately 2184.62 seconds to travel to the flower and back to the hive.
To calculate the time it takes for the bee to travel to the flower and back to the hive, we need to find the total distance the bee travels and divide it by the bee's speed.
Step 1: Calculate the distance traveled by the bee to the flower.
The distance traveled by the bee to the flower is given as 568 m due south. Since the bee is flying directly south, the distance traveled is the magnitude of the displacement and can be calculated using the Pythagorean theorem.
Distance to flower = √(south^2) = √(568^2) = √322,624 = 568 m
Step 2: Calculate the time taken by the bee to travel to the flower.
The bee's speed in still air is 0.71 m/s, and there is a wind blowing toward the south at 0.19 m/s. To calculate the effective speed of the bee in the presence of wind, we use vector addition.
Effective speed = √(speed in still air^2 + wind speed^2)
Effective speed = √(0.71^2 + 0.19^2) = √(0.5041 + 0.0361) = √0.5402 = 0.735 m/s
Time to travel to flower = Distance to flower / Effective speed
Time to travel to flower = 568 m / 0.735 m/s = 773.2 s
Step 3: Calculate the return distance traveled by the bee.
Since the bee is flying back to the hive, the return distance is the same as the distance to the flower, which is 568 m.
Step 4: Calculate the time taken by the bee to return to the hive.
Using the same effective speed, the time taken to return to the hive is:
Time to return = Return distance / Effective speed
Time to return = 568 m / 0.735 m/s = 773.2 s
Step 5: Calculate the total time taken.
To get the total time taken, we add the time taken to travel to the flower and the time taken to return to the hive.
Total time taken = Time to travel to flower + Time to return
Total time taken = 773.2 s + 773.2 s = 1546.4 s
Therefore, it will take the bee approximately 1546.4 seconds to travel to the flower and back to the hive.