An ant walks on a piece of graph paper straight along the x axis a distance of 10.0 cm in 2.20 s. It then turns left 30.0 degrees and walks in a straight line another 10.0 cm in 1.90 s. Finally, it turns another 70.0 degrees to the left and walks another 10.0 cm in 1.60 s.
a)Determine the x component of the ant's average velocity.
b)Determine the y component of the ant's average velocity.
c)Determine the magnitude of ant's average velocity.
d)Determine the direction of ant's average velocity.
To solve this problem, we need to break down the motion of the ant into components and calculate the average values. Let's solve each part step by step.
a) To determine the x-component of the ant's average velocity, we first need to calculate the displacement in the x-direction and the total time taken.
The ant walks along the x-axis a distance of 10.0 cm in 2.20 s and then another 10.0 cm in 1.90 s. So, the total displacement in the x-direction is 10.0 cm + 10.0 cm = 20.0 cm.
The total time taken is 2.20 s + 1.90 s + 1.60 s = 5.70 s.
The x-component of the ant's average velocity is the displacement in the x-direction divided by the total time taken:
x-component of average velocity = 20.0 cm / 5.70 s = 3.51 cm/s.
So, the x-component of the ant's average velocity is 3.51 cm/s.
b) To determine the y-component of the ant's average velocity, we need to calculate the displacement in the y-direction and the total time taken.
The ant turns left 30.0 degrees and then left 70.0 degrees. These turns indicate that the ant changed direction in the y-direction but did not move up or down.
Therefore, there is no displacement in the y-direction, so the y-component of the ant's average velocity is 0 cm/s.
c) To determine the magnitude of the ant's average velocity, we can use the Pythagorean theorem because the average velocity vector is the combination of the x and y components.
Magnitude of average velocity = √(x-component)^2 + (y-component)^2
= √(3.51 cm/s)^2 + (0 cm/s)^2
= √(12.3 cm^2/s^2)
= 3.51 cm/s
So, the magnitude of the ant's average velocity is 3.51 cm/s.
d) To determine the direction of the ant's average velocity, we can use the inverse tangent function (arctan) to calculate the angle.
Direction angle = arctan(y-component/x-component)
= arctan(0 cm/s / 3.51 cm/s)
= arctan(0)
= 0
Therefore, the direction of the ant's average velocity is 0 degrees.
In summary:
a) The x-component of the ant's average velocity is 3.51 cm/s.
b) The y-component of the ant's average velocity is 0 cm/s.
c) The magnitude of the ant's average velocity is 3.51 cm/s.
d) The direction of the ant's average velocity is 0 degrees.