Calculating Boat Ground Speed: E-S Direction

In summary: 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...speed = distance/time
  • #1
Smile101
29
0

Homework Statement


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. Homework Statement
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!
 
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  • #2
Smile101 said:

Homework Statement


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?


For problem 1. You are on the right track, you just need to obtain the correct distance that the plane flew. For this problem the vectors can be connected tip to tail and a right triangle can constructed. Solve this right triangle to obtain the length of the hypoteneuse.
 
  • #3
CFDFEAGURU said:
Smile101 said:

For problem 1. You are on the right track, you just need to obtain the correct distance that the plane flew. For this problem the vectors can be connected tip to tail and a right triangle can constructed. Solve this right triangle to obtain the length of the hypoteneuse.


So I did that and I got the hypotenuse to be approx. 6500m.

How come I heard for average speed it is delta d over delta t? Does this mean total distance covered over total time?

And for average velocity its resultant displacement..so in this case 6500m over total time? Is that true?
 
  • #4
Yes, the total distance divided by the total time is the average velocity.
 
  • #5
CFDFEAGURU said:
Yes, the total distance divided by the total time is the average velocity.


But I thought that was for speed? I'm super confused! aghh... so what would be the answer now?
 
  • #6
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
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
Smile101 said:
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?

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
LowlyPion said:
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.


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
Smile101 said:
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]

If 6500 is the total displacement to the SW, then yes.
 
  • #11
LowlyPion said:
If 6500 is the total displacement to the SW, then yes.

By total displacement do you mean resultant displacement?
 
  • #12
Smile101 said:
By total displacement do you mean resultant displacement?

Yes. The vector addition of 2750 W and 5810 S as Pythagoras would do it.
 
  • #13
LowlyPion said:
Yes. The vector addition of 2750 W and 5810 S as Pythagoras would do it.

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
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
LowlyPion said:
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.

thanks, but i still don't understand what the question is asking me? What does it mean by "ground speed?"
 
  • #16
Smile101 said:
thanks, but i still don't understand what the question is asking me? What does it mean by "ground speed?"

It means the speed that somebody on the ground would see the boat moving at.
 
  • #17
ideasrule said:
It means the speed that somebody on the ground would see the boat moving at.


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

FAQ: Calculating Boat Ground Speed: E-S Direction

1. How do you calculate boat ground speed in the E-S direction?

To calculate boat ground speed in the E-S direction, you will need to use the formula: ground speed = water speed x (cos θ). The water speed is the speed of the boat in still water, and θ is the angle between the direction the boat is moving and the direction of the current.

2. What is the significance of calculating boat ground speed in the E-S direction?

Calculating boat ground speed in the E-S direction allows us to determine the speed and direction in which the boat is actually moving relative to the Earth's surface. This is important for navigation and determining how long it will take to reach a specific destination.

3. How does wind affect boat ground speed in the E-S direction?

Wind can have a significant impact on boat ground speed in the E-S direction. If the wind is blowing in the same direction as the boat is traveling, it can increase the ground speed. However, if the wind is blowing in the opposite direction, it can decrease the ground speed.

4. Can boat ground speed in the E-S direction be calculated using GPS?

Yes, GPS can be used to calculate boat ground speed in the E-S direction. It uses the boat's current location and the time it takes to travel between two points to determine the speed and direction of the boat's movement.

5. What factors can affect the accuracy of boat ground speed in the E-S direction?

There are several factors that can affect the accuracy of boat ground speed in the E-S direction, including wind, current, and the accuracy of the instruments used to measure speed and direction. It is important to regularly calibrate and check these instruments for optimal accuracy.

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