A meteor streaking through the night sky is located with radar. At point A its coordinates are (5.60 km, 1.25 km), and 1.12 s later its has moved to point B with coordinates (6.16 km, 0.900 km).
A. Find the x component of its average velocity between A and B. (in Km/s)
B. Find the y component of its average velocity between A and B.(in Km/s)
C. Find the magnitude of its average velocity between these two points. (in Km/s)
D. Find the direction of its average velocity between these two points. (in degree counterwisefrom +x axis)
To calculate the average velocity between points A and B, we need to find the change in position and the time interval.
A. Find the x component of its average velocity between A and B:
The x component is the change in position in the x direction divided by the time interval. We can use the coordinates (x, y) to find the change in position in the x direction:
Δx = xB - xA = 6.16 km - 5.60 km = 0.56 km
The time interval is given as 1.12 s.
To find the average velocity in the x direction:
Average Velocity (Vx) = Δx / Δt = 0.56 km / 1.12 s = 0.5 km/s
Therefore, the x component of its average velocity between A and B is 0.5 km/s.
B. Find the y component of its average velocity between A and B:
Similarly, we can find the change in position in the y direction using the coordinates (x, y):
Δy = yB - yA = 0.900 km - 1.25 km = -0.35 km
(Note: The negative sign indicates that the meteor moved in the negative y direction.)
To find the average velocity in the y direction:
Average Velocity (Vy) = Δy / Δt = -0.35 km / 1.12 s = -0.3125 km/s
Therefore, the y component of its average velocity between A and B is -0.3125 km/s.
C. Find the magnitude of its average velocity between these two points:
The magnitude of the average velocity can be found using the Pythagorean theorem:
Magnitude = √(Vx^2 + Vy^2) = √(0.5^2 + (-0.3125)^2) = √(0.25 + 0.0977) = √0.3477 = 0.589 km/s
Therefore, the magnitude of its average velocity between points A and B is 0.589 km/s.
D. Find the direction of its average velocity between these two points:
The direction of the average velocity can be found using trigonometry. We can use the arctangent function to find the angle.
Direction (θ) = arctan(Vy / Vx) = arctan(-0.3125 / 0.5) ≈ -32.18 degrees
(Note: The negative sign indicates that the direction is counter-clockwise from the +x axis.)
Therefore, the direction of its average velocity between points A and B is approximately -32.18 degrees counter-clockwise from the +x axis.
To find the average velocity of the meteor between points A and B, we need to calculate the change in position and divide it by the time interval.
A. The x component of average velocity (Vx) can be found using the equation: Vx = (Δx)/(Δt), where Δx is the change in x-coordinate and Δt is the change in time.
Given:
x-coordinate at A (xA) = 5.60 km
x-coordinate at B (xB) = 6.16 km
Time interval (Δt) = 1.12 s
Δx = xB - xA = 6.16 km - 5.60 km = 0.56 km
Vx = (Δx) / (Δt) = 0.56 km / 1.12 s = 0.5 km/s
Therefore, the x component of the average velocity between A and B is 0.5 km/s.
B. Similarly, the y component of average velocity (Vy) can be found using the equation: Vy = (Δy)/(Δt), where Δy is the change in y-coordinate.
Given:
y-coordinate at A (yA) = 1.25 km
y-coordinate at B (yB) = 0.900 km
Δy = yB - yA = 0.900 km - 1.25 km = -0.35 km
Vy = (Δy) / (Δt) = -0.35 km / 1.12 s = -0.313 km/s (rounded to three decimal places)
Therefore, the y component of the average velocity between A and B is approximately -0.313 km/s.
C. The magnitude of the average velocity can be found using the Pythagorean theorem:
|V| = √(Vx^2 + Vy^2)
Using the values obtained,
|V| = √((0.5 km/s)^2 + (-0.313 km/s)^2) = √(0.25 km^2/s^2 + 0.097969 km^2/s^2) = √0.347969 km^2/s^2 = 0.59 km/s (rounded to two decimal places)
Therefore, the magnitude of the average velocity between A and B is approximately 0.59 km/s.
D. The direction of average velocity can be found using the inverse tangent (arctan) function:
Direction (θ) = arctan(Vy / Vx)
θ = arctan((-0.313 km/s) / (0.5 km/s)) = -33.69 degrees (rounded to two decimal places)
Since the direction is measured counterclockwise from the +x axis, the direction of the average velocity between A and B is approximately -33.69 degrees.