a hiker walk due east at 4km per hour and a second hiker starting from the same point walks 55 degree north-east at the rate of 6km per hour. H
ow far apart will they be after 2 hours
the hiker walking east walked 8 km
the hiker walking 55° NE walked 12 km
Since I am not sure what notation of direction you are using,
e.g. is it N55°E OR simply 55° up from the positive x-axis direction OR
I will interpret that the angle between their paths is 55°
So by the cosine law
x^2 = 8^2 + 12^2 - 2(8)(12)cos55°
= 97.87332..
x = √97.87....
=appr 9.89 km
If your angle is different from my interpretation, just make the changes at the end of the equation.
i m having a problem that the angle between north east will be 35 or 55 because if we are considering north east the hiker is moving fom north to east
To find the distance between the two hikers after 2 hours, we can break down their movements into a vector representation.
The first hiker walks due east, which can be represented as a vector with a magnitude of 4 km/h in the positive x-direction (east).
The second hiker walks 55 degrees north-east, which can be represented as a vector with a magnitude of 6 km/h in a direction 55 degrees above the positive x-axis.
Using basic trigonometry, we can find the x and y components of the second hiker's velocity vector:
x-component = cos(55 degrees) * 6 km/h
y-component = sin(55 degrees) * 6 km/h
Now, let's find the total displacement of each hiker after 2 hours:
For the first hiker:
Displacement = (speed) * (time) = 4 km/h * 2 hours = 8 km to the east (x-direction)
For the second hiker:
x-displacement = (x-component velocity) * (time) = cos(55 degrees) * 6 km/h * 2 hours
y-displacement = (y-component velocity) * (time) = sin(55 degrees) * 6 km/h * 2 hours
To calculate the distance between the two hikers, we can use the Pythagorean theorem:
Distance = sqrt( (x-displacement)^2 + (y-displacement)^2 )
Let's now calculate the distance:
x-displacement = cos(55 degrees) * 6 km/h * 2 hours = 6 * cos(55 degrees) * 2 km
y-displacement = sin(55 degrees) * 6 km/h * 2 hours = 6 * sin(55 degrees) * 2 km
Distance = sqrt( (8 km)^2 + (6 * cos(55 degrees) * 2 km)^2 + (6 * sin(55 degrees) * 2 km)^2 )
Calculating this gives us the final answer for the distance between the two hikers after 2 hours.