How Do You Calculate Average Velocity and Relative Air Velocity?

[nando94]

1. A car with an initial direction of north moves clockwise one quarter a circle of radius 30 m in 15 s at a constant speed. What is the average velocity?

a) 1 m/s north
b) 1.41 m/s northeast
c) 1.57 m/s southwest
d) 2.83 m/s northeast

displacement/total time = avg velocity

15pi/15s = pi = 3.14 m/s

but none of the answer choice are 3.14 m/s. also how do you find the direction?

2. The velocity of a jet with respect to the ground is 200 m/s at an angle of 30 degrees north of east. The velocity of the jet with respect to the air is 150 m/s at an angle of 60 degrees north of east. What is the velocity of the air with respect to the ground?

a) 102 m/s 17 degrees south of east
b) 134 m/s 49 degrees south of east
c) 134 m/s at 17 degrees north of east
d) 203 m/s at 65 degrees north of east
e) 112 m/s at 50 degrees north of east


I the jets velocity into its components and got vy = 100 and vx = 173. Then with respect to the air vy = 130 vx = 75.

Then i took the sqrt of (173 - 130)^2 + (100 - 75) ^ to get 103 m/s but I think I am doing something wrong.

 

[haruspex]

displacement/total time = avg velocity

15pi/15s = pi = 3.14 m/s

but none of the answer choice are 3.14 m/s. also how do you find the direction?

Velocity is a vector. It's the change in the position vector divided by the time.
What is the change in the position vector?

2. The velocity of a jet with respect to the ground is 200 m/s at an angle of 30 degrees north of east. The velocity of the jet with respect to the air is 150 m/s at an angle of 60 degrees north of east. What is the velocity of the air with respect to the ground?

a) 102 m/s 17 degrees south of east
b) 134 m/s 49 degrees south of east
c) 134 m/s at 17 degrees north of east
d) 203 m/s at 65 degrees north of east
e) 112 m/s at 50 degrees north of east


I the jets velocity into its components and got vy = 100 and vx = 173. Then with respect to the air vy = 130 vx = 75.

Then i took the sqrt of (173 - 130)^2 + (100 - 75) ^ to get 103 m/s but I think I am doing something wrong.

Yes, you're mixing up the vx's with the vy's. Try again, making sure you only take differences of speeds in the same direction.