I need some clarification for a high school vectors question (accelerating bird)

[Christopher Nguyen]

Homework Statement

A bird flying in the air accelerates 2.82 m/s² north for 4.11 seconds. the final velocity of the bird is 9.09 m/s [east]. What was the initial velocity of the bird?

Homework Equations

v_f=v₀+a*t

v_(average)=(v₀+v_f)/2

v=d/t

d=v₀t +½at²

tanθ=opp/adj

The Attempt at a Solution

[/B]
I turned the givens into vectors that resulted in the formation of a right angle triangle.

Used Pythagorean theorem to solve for the hypotenuse (initial velocity).

Used tangent to solve for the angle

The one question I have is regarding the vector for acceleration that would be used: when turning the acceleration into a velocity (vector) would the final velocity or the average velocity be used?

I used the average velocity with the idea that if the final were used then it would be the same as if a constant vector were applied to the bird (which is not the case). Since the force varies the vector should only apply the final velocity at the end of the 4.11s.

Can someone help clarify if this is the wrong approach or not?

Thank you.

(edit: sorry for the Ms paint and thank you for the tips for formatting)

 

[Orodruin]

You have just described in words what you did. In order to avoid misunderstandings, it is better if yoy also show your actual computations (also the intermediate steps).

A hint is that only your first relevant equation is actually relevant to your problem.

 

[PeroK]

Homework Statement

A bird flying in the air accelerates 2.82 m/s² north for 4.11 seconds. the final velocity of the bird is 9.09 m/s [east]. What was the initial velocity of the bird?

Homework Equations

v_f=v₀+a*t

v_(average)=(v₀+v_f)/2

v=d/t

d=v₀t +½at²

tanθ=opp/adj

The Attempt at a Solution

[/B]
I turned the givens into vectors that resulted in the formation of a right angle triangle.

Used Pythagorean theorem to solve for the hypotenuse (initial velocity).

Used tangent to solve for the angle

The one question I have is regarding the vector for acceleration that would be used: when turning the acceleration into a velocity (vector) would the final velocity or the average velocity be used?

I used the average velocity with the idea that if the final were used then it would be the same as if a constant vector were applied to the bird (which is not the case). Since the force varies the vector should only apply the final velocity at the end of the 4.11s.

Can someone help clarify if this is the wrong approach or not?

Thank you.

To answer your question, why would you use average velocity? What are you trying to calculate?

You have a quoted a number of equations, but you haven't indicated that these are vector equations, and you have not related them to separate vector components.

 

[Christopher Nguyen]

To answer your question, why would you use average velocity? What are you trying to calculate?

You have a quoted a number of equations, but you haven't indicated that these are vector equations, and you have not related them to separate vector components.

Sorry about the lack of visuals. The question is about trying to solve for an initial velocity when it is accelerated by 2.82m/s² for 4.11 seconds and whether the final velocity or average velocity should be used as the added component.

 

[PeroK]

Sorry about the lack of visuals. The question is about trying to solve for an initial velocity when it is accelerated by 2.82m/s² for 4.11 seconds and whether the final velocity or average velocity should be used as the added component.

Yes, and my question to you is why use average velocity?

Try some calculations with simpler numbers if you need to.

 

[sojsail]

You have an acceleration to the North, and after 4.11 s you have a final velocity to the East. It is asking about the initial velocity. You might think about why there is no velocity to the North after the 4.11 s. Did the acceleration affect whatever initial velocity there was to the East?

 

[Christopher Nguyen]

Yes, and my question to you is why use average velocity?

Try some calculations with simpler numbers if you need to.

I used the average velocity because the final velocity of the acceleration wouldn't be applied to the initial velocity for the entire duration of the 4.11s.

This idea could be misguided and I would like to know if it is and why.

 

[PeroK]

I used the average velocity because the final velocity of the acceleration wouldn't be applied to the initial velocity for the entire duration of the 4.11s.

This idea could be misguided and I would like to know if it is and why.

Yes, it's misguided. Try this one. It's a 1D problem:

A bird accelerates at $2m/s^2$ for $4s$. It's final velocity is $8m/s$. What was its initial velocity?

 

[Christopher Nguyen]

You have an acceleration to the North, and after 4.11 s you have a final velocity to the East. It is asking about the initial velocity. You might think about why there is no velocity to the North after the 4.11 s. Did the acceleration affect whatever initial velocity there was to the East?

the acceleration would have counteracted an initial component of the initial velocity that was towards the south would it not?

the acceleration doesn't affect the initial velocity to the east so that component still exists which is why the final velocity lies towards the east

 

[Christopher Nguyen]

Yes, it's misguided. Try this one. It's a 1D problem:

A bird accelerates at $2m/s^2$ for $4s$. It's final velocity is $8m/s$. What was its initial velocity?

v₀=8-(2)(4)=0 m/s

 

[PeroK]

v₀=8-(2)(4)=0 m/s

So, you used the final velocty and not the average velocity.

 

[Christopher Nguyen]

So, you used the final velocty and not the average velocity.

I get it.

i additionally had a proof where i correlated velocity with displacement and converted all of the components with their respective displacement during the time period. (its definitely wrong because i got the same answer) could you help me fix that as well?

 

[PeroK]

I get it.

i additionally had a proof where i correlated velocity with displacement and converted all of the components with their respective displacement during the time period. (its definitely wrong because i got the same answer) could you help me fix that as well?

I'm not sure why you'd need displacement. It's a simple equation involving velocity and acceleration.

 

[Christopher Nguyen]

I'm not sure why you'd need displacement. It's a simple equation involving velocity and acceleration.

it was just a "proof", not part of the actual question. I thought since displacement and velocity were correlated with time i could use that fact to "prove" the solution i got.

 

[Ray Vickson]

it was just a "proof", not part of the actual question. I thought since displacement and velocity were correlated with time i could use that fact to "prove" the solution i got.

View attachment 240619

Displacement has nothing to do with this problem. The problem is about velocities and acceleration. Attempting to introduce some type of displacement equation in order to prove something about velocity just indicates that you do not understand this problem---other problems, maybe, but not this one.