Two hikers are wandering through heavy woods with walkie talkies. The walkie talkies have a range of 0.0568182 miles. From their starting point, they head off at an angle of 109.167° of each other. Hiker 1 walks 0.24 miles per hour, hiker 2 walks 0.17 miles per hour. If each continues to go straight, how long will it be before they can no longer communicate?

Can someone tell me the formula(s) to use? Please don't give the answer! Thank you!

after t hours, the distance d between the hikers is

d^2 = (.24t)^2 + (.17t)^2 - 2(.24t)(.17t)cos109.167°

so, find t when d = 0.0568182

I get about 10 minutes.

The radios aren't much use, I guess...

Given: 1000ft of range, H1 walks 1267.2ft per hour, H2 walks 897.6ft per hour, and walk from each other at approximately 109.17° angle

So to get to where b= 1000 I subtracted equally from both a(897.6) and c(1267.2) and have concluded to reach ~1001ft. Side a=415.1(H2), c= 784.7(H1)
b=√a^2+c^2-2ac*cos(B)
b= √415.1^2+784.7^2-2(415.1*784.7)*cos(109.17)
b= √172308.01+615754.09-651457.94*-.32832 →b= √788062.1+213888.4106
b= √1001950.511 →b=~ 1000.98(rounded up from 1000.97478)
For Hiker2; 897.6/x= 415.6 →60/2.15976= 27.78086
For Hiker1; 1267.2/x= 784.7 →60/1.61488= 37.15446
For Hiker2 it will take approximately 28mins, and for Hiker1 it will take approximately 37mins.
Hope this helps!

Why did the scarecrow win an award? Because he was outstanding in his field! Now, let's get back to the question.

To find out how long it will take before the hikers can no longer communicate, we can use a bit of trigonometry. We can break down the motion of each hiker into horizontal and vertical components, then calculate their positions over time.

Here are a few formulas you can use:

1. To calculate the x-coordinate of Hiker 1's position after time t:
x₁ = (Hiker 1's speed) * t

2. To calculate the y-coordinate of Hiker 1's position after time t:
y₁ = 0 (since Hiker 1 walks in a straight line)

3. To calculate the x-coordinate of Hiker 2's position after time t:
x₂ = (Hiker 2's speed) * t * cos(109.167°)

4. To calculate the y-coordinate of Hiker 2's position after time t:
y₂ = (Hiker 2's speed) * t * sin(109.167°)

5. To calculate the distance between Hiker 1 and Hiker 2 at time t:
distance = sqrt((x₂ - x₁)² + (y₂ - y₁)²)

Keep in mind that if the calculated distance is greater than the range of the walkie talkies (0.0568182 miles), they will no longer be able to communicate.

Give it a try, and feel free to ask if you have any more questions! Remember, laughter is the best hiking companion.

To solve this problem, we can use the concept of distance and time.

First, let's calculate how far each hiker can walk in one hour. Hiker 1 walks at a speed of 0.24 miles per hour, so in one hour, they will be 0.24 miles away from their starting point. Similarly, Hiker 2 walks at a speed of 0.17 miles per hour, so in one hour, they will be 0.17 miles away from their starting point.

Now, let's consider the relative motion between the two hikers. They are moving at an angle of 109.167° to each other. This means they are forming a triangle with their starting point as the common vertex.

To find the distance between the two hikers after one hour, we can use the Law of Cosines. The formula for the Law of Cosines is:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where:
- c is the distance between the two hikers
- a and b are the distances each hiker can walk in one hour
- C is the angle between the two distances (109.167° in this case)

Using the formula, we can calculate the distance between the two hikers after one hour.

Please note that this formula assumes the hikers are continuously moving in a straight line. In reality, they may change direction or encounter obstacles that would impact their communication range.