please check:
An ant on a picnic table travels 3.0 * 10^1 cm eastward, then 25 cm northward, and finally 15 cm westward. What is the magnitude of the ant's displacement relative to its original position
i got 70 cm
please help with this:
For the winter, a duck flies 10.0 m/s due south against a gust of wind with a speed of 2.5 m/s. What is the resultant velocity of the duck?
:)
29cm at 59 degress North of East
For the first one, I don't think it would be as much as 70 cm because as you're moving, you make an almost complete shape of a trapezoid. When it says "relative to its original position", it means from the starting point you find the distance, so it'll be I think around 30 cm but you'll probably have to be more exact.
For the second problem, you also find the difference between the two velocities to find the resultant velocity of the duck. Here, the duck's velocity would be 7.5 m/s because the wind is slowing him down.
Emily is a physics whiz.
7.5 m/s south?
Haha thanks :)
for the first one find the amount moved total east west.
Movement lateral=(east)- (west)
30cm - 15cm = 15 cm
now find the longitudinal movement
Movement longitudinal = 25 cm
the maginitude is the distance moved relative to original postion which is given by the distance formula
d= (x^2 + y^2)^(1/2)
where x is movement lateral and y is movement longitudinal
d= (15^2 + 25^2)^(1/2)
correct
You all are really helpful. I am taking AP physics currently and don't understand much. Thanks sm Emily and Das for the tips and help!
To find the magnitude of the ant's displacement, we can use the Pythagorean theorem. The ant traveled 3.0 * 10^1 cm eastward (in the positive x-direction), then 25 cm northward (in the positive y-direction), and finally 15 cm westward (in the negative x-direction).
First, calculate the displacement in the x-direction:
Displacement in x-direction = 3.0 * 10^1 cm - 15 cm = 30 cm - 15 cm = 15 cm (positive because it's eastward)
Next, calculate the displacement in the y-direction:
Displacement in y-direction = 25 cm
Using the Pythagorean theorem, the displacement can be found using the formula:
Displacement = √(Displacement in x-direction)^2 + (Displacement in y-direction)^2
Substituting the values, we get:
Displacement = √(15 cm)^2 + (25 cm)^2
Displacement = √225 cm^2 + 625 cm^2
Displacement = √850 cm^2
Displacement ≈ 29.15 cm
Hence, the magnitude of the ant's displacement relative to its original position is approximately 29.15 cm.
Now let's move on to the next question:
To calculate the resultant velocity of the duck, we need to consider the vector addition of the duck's velocity and the wind's velocity.
The duck is flying at 10.0 m/s due south. Since it is moving against the gust of wind, the wind's velocity would be in the opposite direction, which is northward. The magnitude of the wind's velocity is given as 2.5 m/s.
Since the velocities are in opposite directions, we subtract the magnitudes to obtain the resultant velocity:
Resultant velocity = Magnitude of duck's velocity - Magnitude of wind's velocity
Resultant velocity = 10.0 m/s - 2.5 m/s
Resultant velocity = 7.5 m/s
Therefore, the resultant velocity of the duck is 7.5 m/s.
70 cm is the distance, not displacement. His travels are vectors, and you have to add them as vectors.
He is flying at 10relative to the wind, but the wind is pushing him back at 2.5.
HMMMM. What do you think.