What is the magnitude of the resultant velocity for a bird flying first at a speed of 10m/s North East and then flying to south at a speed of 8m/s?
Draw the vectors. All you need here is the 3rd side of the triangle.
Use the law of cosines.
x^2 = 10^2 + 8^2 - 2*10*8*cos45°
answer
Va=10cos45 E + 10 sin45 N
Vb=-8N
VresultN=Va+Vb=10*.707-8 N=7.07-8 N= .93S
Vreslt= Vn + 10*.707E
magnitude= sqrt(.93^2 + 7.07^2)
All angles are measured CW from +y-axis.
Vr = 10m/s[45o] + 8m/s[180o].
X = 10*sin45 + 8*sin180 = 7.07 m/s.
Y = 10*Cos45 + 8*Cos180 = -0.93 m/s.
Vr = sqrt(X^2+Y^2).
7.13
Well, well, well! Looks like this bird can't make up its mind, flying in different directions like that! But fear not, my friend, I'm here to help you out with some humor.
To find the magnitude of the resultant velocity, we first need to determine the resultant velocity vector. In simpler terms, we need to add these two velocities together.
Now, if we draw a diagram, we can see that the bird initially flies at 10m/s in the Northeast direction, which we can split into equal North and East components. And then it flies directly South at 8m/s. So, let's crunch some numbers!
Using a bit of trigonometry, we can find that the North and South components cancel each other out, leaving us only with the East component.
Therefore, the magnitude of the resultant velocity is 8m/s, pointing East!
So, this bird may have started off a bit indecisive, but in the end, it's heading straight East at a steady pace. Just like a true bird on a mission!
Remember, if you have any more questions or need more laughs, I'm here for you!
To find the magnitude of the resultant velocity for the bird, we need to combine its initial velocity and its final velocity using vector addition.
Let's start by representing the bird's initial velocity graphically. The bird is flying at a speed of 10m/s in the North East direction. We can represent this velocity as a vector with a magnitude of 10m/s and a direction of 45 degrees north of east.
Next, we need to represent the bird's final velocity graphically. The bird is flying at a speed of 8m/s in the south direction. We can represent this velocity as a vector with a magnitude of 8m/s and a direction of 180 degrees (opposite to the north direction).
To add these two vectors, we can draw them tail-to-tip. Starting from the tail of the first vector (10m/s North East), we draw the second vector (8m/s South) such that the tail of the second vector is connected to the tip of the first vector.
Now, we can draw a third vector from the tail of the first vector to the tip of the second vector. This third vector represents the resultant velocity of the bird.
To find the magnitude of the resultant velocity, we can use the Pythagorean theorem. The magnitude of the resultant velocity is equal to the square root of the sum of the squares of the magnitudes of the two combined vectors. In this case, it can be calculated as:
Resultant velocity = sqrt((10^2) + (8^2)) = sqrt(164) ≈ 12.81 m/s.
Therefore, the magnitude of the resultant velocity for the bird is approximately 12.81 m/s.