You drive a car 1500 ft to the east, then 2500 ft to the north. If
the trip took 3.0 minutes, what were the direction and magnitude of your average velocity?
final displacement: d = 500√34
avg speed: d/3 ft/min
direction: tanθ = 2500/1500 = 5/3
direction of average velocity is 59 north of east
and magnitude of average velocity is 4.2 m/s
To find the direction and magnitude of your average velocity, you need to calculate the displacement and divide it by the total time.
First, let's calculate the displacement. Since you drove 1500 ft to the east and then 2500 ft to the north, you need to find the resultant displacement. We can use the Pythagorean theorem to calculate the magnitude of the displacement:
Displacement (d) = √(1500^2 + 2500^2)
Next, we can calculate the average velocity by dividing the displacement by the total time:
Average Velocity (v) = Displacement (d) / Total Time
Now, let's substitute the values:
Magnitude of Displacement (d) = √(1500^2 + 2500^2)
Total Time = 3.0 minutes
Magnitude of Displacement (d) = √(2250000 + 6250000)
Magnitude of Displacement (d) = √8500000
Magnitude of Displacement (d) ≈ 2915.48 ft
Average Velocity (v) = 2915.48 ft / 3.0 minutes
Average Velocity (v) ≈ 971.83 ft/min
So, your average velocity was approximately 971.83 ft/min.
To determine the direction of the average velocity, we need to find the angle with respect to the positive x-axis. We can use trigonometry to calculate this angle:
angle = arctan(2500 / 1500)
angle ≈ 59.04 degrees
Therefore, the direction of your average velocity is approximately 59.04 degrees with respect to the positive x-axis.