Two normads leaves camp at the same time,one walks 5km/h on a bearing of 39 degree and the other walks 7.5km/h on a bearing of 265 degree after 2 hours.how far are apart and what is the bearing of the second from the first?
To find the distance and bearing between the two nomads, we can use vector addition and trigonometry.
First, let's calculate the displacement vectors for each nomad after 2 hours of walking:
Nomad 1:
Distance = 5 km/h * 2 hours = 10 km
Bearing = 39 degrees
Nomad 2:
Distance = 7.5 km/h * 2 hours = 15 km
Bearing = 265 degrees
Now, let's convert the bearing angles into Cartesian coordinates using trigonometry.
Nomad 1:
x1 = 10 km * cos(39 degrees)
y1 = 10 km * sin(39 degrees)
Nomad 2:
x2 = 15 km * cos(265 degrees)
y2 = 15 km * sin(265 degrees)
Next, let's calculate the resultant displacement vector by adding the individual displacement vectors:
Resultant Displacement:
x = x1 + x2
y = y1 + y2
Now, we can find the distance between the two nomads using the magnitude of the resultant displacement vector:
Distance = √(x^2 + y^2)
Finally, to find the bearing of the second nomad from the first, we can use trigonometry once again:
Bearing = atan2(y, x)
By plugging in the values and performing the calculations, we can determine the distance and bearing:
Distance = √((x1 + x2)^2 + (y1 + y2)^2)
Bearing = atan2(y1 + y2, x1 + x2)
Please note that the calculations involve trigonometric functions and vector addition.
I see that you corrected your post, and inserted a time of 2 hours
So go back to my previous reply to the same question, replace t with 2
and repeat the steps.
(or just plug t=2 into my answer for x)