Two nomads leave camp at the same time.One walks at 5km\h on a bearing 039°.The other walks at 7.5km\h on a bearing 265°.After two hours how far apart are they and what is the bearing of the second from the first?
they walk on a HEADING, not a bearing.
distance = speed * time
So draw the diagram, and then use the law of cosines to find the distance.
For the bearing, use the law of sines to then find the angle at nomad #1.
If it is θ, then the bearing is 180+39+θ
To find the distance and bearing between the two nomads after two hours, we can use the concept of vectors.
Step 1: Calculate the displacements of each nomad using their respective speeds and the time of 2 hours.
Nomad 1 displacement = speed * time = 5 km/h * 2 h = 10 km
Nomad 2 displacement = speed * time = 7.5 km/h * 2 h = 15 km
Step 2: Convert the bearing angles to degrees.
Bearing 039° in degrees = 39°
Bearing 265° in degrees = 265°
Step 3: Determine the resultant displacement of each nomad using trigonometry.
Nomad 1 resultant displacement = 10 km * cos(39°) = 7.67 km
Nomad 2 resultant displacement = 15 km * cos(265°) = -7.07 km
Note: The negative sign indicates the opposite direction.
Step 4: Calculate the distance between the two nomads using the Pythagorean theorem.
Distance = sqrt((7.67 km)^2 + (-7.07 km)^2) = sqrt(58.97 km^2) ≈ 7.68 km
Step 5: Calculate the bearing angle of the second nomad from the first nomad using trigonometry.
Bearing = arctan( |Nomad 2 displacement| / |Nomad 1 displacement| )
Bearing = arctan(7.07 km / 7.67 km) ≈ 42.85°
Therefore, after two hours, the two nomads are approximately 7.68 km apart, and the bearing of the second nomad from the first nomad is approximately 42.85°.
To find the distance between the two nomads after two hours, we can use the formula: distance = speed × time.
For the first nomad walking at 5 km/h, after two hours, the distance covered would be 5 km/h × 2 h = 10 km.
For the second nomad walking at 7.5 km/h, after two hours, the distance covered would be 7.5 km/h × 2 h = 15 km.
Now we have the distances covered by each nomad. To find the distance between them, we can use the Pythagorean theorem, as the two nomads are moving at different angles.
Using the Pythagorean theorem: distance = √(a^2 + b^2), where a and b are the distances covered by each nomad.
So, distance = √(10^2 + 15^2) = √(100 + 225) = √325 ≈ 18.03 km.
Therefore, after two hours, the two nomads are approximately 18.03 km apart.
To find the bearing of the second nomad from the first, we can use the concept of relative bearing.
The bearing of the second nomad from the first can be found by subtracting the bearing of the first nomad from the bearing of the second nomad. However, we need to convert the bearings to the same reference direction.
The bearing of the first nomad is given as 039°. To convert this to a common reference point, we subtract it from 360°: 360° - 039° = 321°.
Now we can find the relative bearing of the second nomad from the first by subtracting the bearings: 265° - 321° = -56°.
However, negative bearings are not commonly used; to convert it to a positive angle, we add 360°: -56° + 360° = 304°.
Therefore, after two hours, the bearing of the second nomad from the first is approximately 304°.