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. this is my ques but .i am having problem that if the hiker walks 55 degree north east so if we consider the axis of direction the angle between north east will be 90 so two angle will form 35 degree and 55 degree so which angle we should consider
I answered this question for somebody called bushra on Friday
http://www.jiskha.com/display.cgi?id=1360926983
are you the same person?
If so, why didn't you do the calculation for the alternate interpretation and compare the answers probably supplied in your text ?
To solve this problem, we can break it down into two components: the east-west component and the north-south component.
First, let's find the distance traveled by the first hiker after 2 hours. Since the hiker walks due east at 4 km per hour, they would have traveled 4 km/h * 2 h = 8 km horizontally.
Next, let's find the distance traveled by the second hiker after 2 hours. The hiker is walking at 55 degrees northeast at 6 km per hour. To determine the distance traveled northwards, we can use trigonometry. The angle between the north direction and the direction the hiker is walking is 90 - 55 = 35 degrees. Using the sine function, we can find the distance traveled northwards as sin(35 degrees) * (6 km/h * 2 h) = 6 km/h * 2 h * 0.5736 = 6.8832 km.
Now, let's find the distance traveled eastwards by the second hiker. The angle between the east direction and the direction the hiker is walking is 55 degrees. Again using trigonometry, we can find the distance traveled eastwards as cos(55 degrees) * (6 km/h * 2 h) = 6 km/h * 2 h * 0.5736 = 6.8832 km.
To find the total distance between the two hikers, we use the Pythagorean theorem. The horizontal distance is 8 km, the distance traveled northwards is 6.8832 km, and the distance traveled eastwards is 6.8832 km. Therefore, the total distance between the two hikers after 2 hours is sqrt((8 km)^2 + (6.8832 km)^2 + (6.8832 km)^2) = sqrt(64 km^2 + 47.4747 km^2 + 47.4747 km^2) = sqrt(158.9494 km^2) ≈ 12.615 km.
Therefore, after 2 hours, the hikers will be approximately 12.615 km apart.