if he travels 7km N 30 degree E and 10km east find the resultant displacement
All angles are measured CW from +Y-axis.
Disp. = 7km[30o] CW + 10km[90o] CW.
X = 7*sin30 + 10*sin90 = 13.5 km.
Y = 7*Cos30 + 10*Cos90 = 6.06 km.
Disp. = Sqrt(X^2 + Y^2) = 14.8 km.
You can draw the resultant from the tail of the first vector to the head of the second vector, and then use Trigonometry to solve it : )
What is the direction of the displacement?
Answers
Well, isn't that just a fancy way of saying he's going in a funny zigzag? It's like trying to find your way through a corn maze! Let me put on my clown hat and calculate this for you.
First, let's break down his travel into two components:
1. 7 km north 30 degrees east: Now, if he's going north and a little bit to the east, it's like he's climbing a mountain and trying to catch the sunset at the same time. The northward component is 7 km * sin(30°) and the eastward component is 7 km * cos(30°).
2. 10 km east: Ah, pure straightforward travel! No funny angles here. It's just a good old-fashioned walk to the east.
Now, let's add up those components and find the resultant displacement. Mathematically, the resultant displacement is the square root of the sum of the squares of the components:
Resultant displacement = √((7 km * sin(30°) + 10 km)^2 + (7 km * cos(30°))^2)
I could give you the exact numerical result, but where's the fun in that? Let's just say that the resultant displacement will be as twisted and convoluted as a circus clown's sense of direction!
To find the resultant displacement, we first need to break down the given directions into their respective components.
1. Traveling 7 km north means we have a northward component of 7 km.
2. Traveling 30 degrees east of north means we have a northeast component. To find the northeast component, we can use trigonometry. The northeast component can be determined by multiplying the northward component by the cosine of the angle. Cosine(30) is √3/2. Therefore, the northeast component is (7 km) * (√3/2).
3. Traveling 10 km east implies a purely eastward component of 10 km.
Now that we have the respective northward and eastward components, we can find the resultant displacement by using the Pythagorean theorem.
Resultant displacement = √((northward component)^2 + (eastward component)^2)
Plugging in the values, the resultant displacement is:
Resultant displacement = √((7 km)^2 + ((7 km) * (√3/2))^2 + (10 km)^2)
Simplifying the equation gives the final answer for the resultant displacement.