Nikki and Laura are standing on opposite sides of a hive of killer bees. The bees can fly 7.5 m in sec
still air, and the wind is blowing 4.5 m in the indicated direction. Notice that if the bees are flying sec
upwind (against the wind), then the wind speed will decrease their ground speed. Likewise, if the bees are flying downwind (with the wind), then the wind will increase their ground speed. Two bees leave the hive; one is heading for Nikki and the other toward Laura. Assume that both women start running away from the hive at the same instant.
(a) What is the ground speed of each bee? m
(b) Assume each person runs 3.1sec. Determine who escapes and who doesn't. If some- one can't escape, determine where and when the attack will occur.
(c) Determine the minimum speed each must run in order to avoid being stung. Is it realistic for Nikki to outrun the bees? How about Laura? (It may help to know that 1 mile = 1609.34 meters
so, what is the indicated direction?
Anyway, draw the velocity vectors and solve for the missing speed/direction.
nikki is 20m left from the hive, laura is 26m right from the hive and the wind is blowing to the right
how would i solve it now?
To determine the ground speed of each bee, we need to account for the effect of the wind on their motion.
(a) Ground speed of each bee:
Since the wind is blowing in a specific direction, it affects the bees' movement differently depending on whether they are flying upwind or downwind.
Let's assume the bee heading towards Nikki is flying upwind. In this case, the wind speed will decrease its ground speed. To calculate the ground speed, we need to subtract the wind speed from the bee's flying speed.
Ground speed of the bee heading towards Nikki = Bee's flying speed - Wind speed
= 7.5 m/s - 4.5 m/s
= 3 m/s
Similarly, let's assume the bee heading towards Laura is flying downwind. In this case, the wind speed will increase its ground speed. To calculate the ground speed, we need to add the wind speed to the bee's flying speed.
Ground speed of the bee heading towards Laura = Bee's flying speed + Wind speed
= 7.5 m/s + 4.5 m/s
= 12 m/s
So, the ground speed of the bee heading towards Nikki is 3 m/s, and the ground speed of the bee heading towards Laura is 12 m/s.
(b) Determining who escapes and who doesn't:
To determine who escapes and who doesn't, we need to compare the distances each person runs in the given time of 3.1 seconds with the distance covered by the bees.
Let's start with Nikki. The distance she covers in 3.1 seconds can be calculated using the formula:
Distance = Speed × Time
Distance covered by Nikki = Nikki's ground speed × Time
= 3 m/s × 3.1 s
= 9.3 m
Similarly, the distance covered by the bee heading towards Nikki would be:
Distance covered by the bee = Bee's ground speed × Time
= 3 m/s × 3.1 s
= 9.3 m
Since the distance covered by Nikki and the bee are the same, they will meet at the same point at the same time.
Now let's consider Laura. The distance she covers in 3.1 seconds can be calculated in the same way:
Distance covered by Laura = Laura's ground speed × Time
= 12 m/s × 3.1 s
= 37.2 m
Again, the distance covered by the bee heading towards Laura would be:
Distance covered by the bee = Bee's ground speed × Time
= 12 m/s × 3.1 s
= 37.2 m
Since the distance covered by Laura and the bee are the same, they will also meet at the same point at the same time.
So, both Nikki and Laura will be attacked by the bees at the same location after 3.1 seconds.
(c) Determining the minimum speed each must run to avoid being stung:
In order to avoid being stung, Nikki and Laura need to run faster than the ground speed of the bees.
For Nikki to outrun the bee heading towards her, she needs to run faster than 3 m/s. Let's convert this to miles per hour for easier comparison:
Nikki's minimum speed = 3 m/s × 2.23694 (conversion factor to mph)
= 6.71 mph
For Laura to outrun the bee heading towards her, she needs to run faster than 12 m/s. Converting this to mph:
Laura's minimum speed = 12 m/s × 2.23694
= 26.83 mph
So, Nikki needs to run at least 6.71 mph to outrun the bee, while Laura needs to run at least 26.83 mph.
Given that the average human running speed ranges between 5-12 mph, it may be unrealistic for Nikki to outrun the bee unless she is an exceptional runner. On the other hand, Laura would need to be an extremely fast runner to avoid being stung.
You don't say which girl is to the right or the left. You really left out a lot of vital information didn't you?
(a) the bee's ground speed is
7.5 + 4.5 = 12 m/s downwind
7.5 - 4.5 = 3.0 m/s upwind
I'll assume that Nikki is upwind and Laura is downwind. If that's not the case, then just reverse things as needed.
For the bees to catch Laura in less than 3.1 seconds, we need
12*3.1 >= 26 + 3.1L
Laura must run at least 3.61 m/s
For Nikki,
3*3.1 >= 20 + 3.1N
Nikki can stand still, since the bees only make it 9.3m in the time allotted.