# Vector Problems

1. Jul 4, 2009

### Smile101

1. The problem statement, all variables and given/known data
A plane flies 2750 m[W] in 25s and then 5810m in 67s

a) What is the average speed of the plane?
b) What is the average velocity of the plane?

I tried doing it and I don't know if I'm right. My physics teacher can't explain anything for beans so could you please explain the processes you go through while trying to achieve your answer. My teacher never gave me any formulas so..here's my attempt...

Vav= Distance/time??? so 5810-2750/67-25??
Vav(velocity)= v1+v2/2 soo -2750+(-5810)/2???

2. The problem statement, all variables and given/known data
Determine the ground speed of a boat which can go at 25km/h, but is traveling [E] in a river that flows at 5km/h .

I have no clue what this question is asking nor what to do!! pleaseeee help!

Last edited: Jul 4, 2009
2. Jul 4, 2009

3. Jul 4, 2009

4. Jul 4, 2009

### CFDFEAGURU

Yes, the total distance divided by the total time is the average velocity.

5. Jul 4, 2009

### Smile101

But I thought that was for speed? I'm super confused!! aghh... so what would be the answer now?

6. Jul 4, 2009

### CFDFEAGURU

Speed and velocity are the same. They are a distance divided by a time. Thier units are Meters/second or in the USA Miles/Hour.

7. Jul 4, 2009

### Smile101

So the average speed is going to be 2750 + 5810/ 27+ 65 which is 93m/s ??

The average velocity would be -2750 + (-5810) / 27+ 65 which is 93m/s (SW)
Is it right that i added the signs for the velocity?

8. Jul 4, 2009

### LowlyPion

I think your confusion is in the definition of speed and velocity.

Think of speed as a scalar. It is the instantaneous rate of change of displacement. So for the average speed, they want the total distance traveled divided by the total time.

Speed_avg = (V1*T1 + V2*T2)/(T1 + T2)

But velocity is something slightly different. Velocity is a vector. That carries distance and direction with it. When they ask for average Velocity what they want is total displacement divided by total time.

As an example if I run like a jack rabbit from my porch to the mailbox and back at 15 m/s each way, then you could say my average speed is 15 m/s. But if you want my average velocity for the trip ... well my total displacement is 0 ... so my average velocity is also 0.

9. Jul 4, 2009

### Smile101

Oh thanks, that makes more sense. So in the case of problem 1, I would take the resultant displacement- 6500m/ 92s (27 + 65) = 70.7 m/s [SW]

10. Jul 4, 2009

### LowlyPion

If 6500 is the total displacement to the SW, then yes.

11. Jul 4, 2009

### Smile101

By total displacement do you mean resultant displacement?

12. Jul 4, 2009

### LowlyPion

Yes. The vector addition of 2750 W and 5810 S as Pythagoras would do it.

13. Jul 4, 2009

### Smile101

okay thanks. One more question.. well actually 2.. if someone knows how to solve problem 2 i would really appreciate knowing how!

Average velocity is taken care of now but average speed you you subtract d2-d1 or add d1+d2? Same would go for time...

14. Jul 4, 2009

### LowlyPion

Sorry, didn't see the second question.

That's a frame of reference problem. In the frame of reference of the river the boat travels East. The river flows South, if you are standing on shore.

The velocities here are vectors that you would add as before, if you want the velocity in the frame of the person on shore. (That's what ground speed implies.)

Once you determine the velocity, then all they want is the speed, which is merely the |velocity|, and no direction needs to be calculated.

Remember speed is instantaneous velocity. It is the scalar magnitude of the velocity vector at any point.

15. Jul 4, 2009

### Smile101

thanks, but i still don't understand what the question is asking me? What does it mean by "ground speed?"

16. Jul 4, 2009

### ideasrule

It means the speed that somebody on the ground would see the boat moving at.

17. Jul 4, 2009

### Smile101

thank you! :) And to everyone else that helped! :)