How much distance did the fly cover?

[Delta31415]

Homework Statement

You have two cars traveling on a course to crash into each other, a fly is on one of the cars. The question is how much distance does the fly cover until the cars crash?
V= velocity,t=time
Df=?
p/v1,v2
lets say the cars are traveling at the same speed

This is a sketch of the problem

Homework Equations

http://images.tutorvista.com/cms/formulaimages/83/instantaneous-velocity-formulas.PNG

The Attempt at a Solution

v(t)= at + c

[/B]

 

[haruspex]

Your diagram shows three velocities. Please explain what those are and post some attempt.

 

[Delta31415]

i have been trying to slove this thing for the past 5 hours and i don't understand one bit of it so please don't blame and me

 

[haruspex]

i have been trying to slove this thing for the past 5 hours and i don't understand one bit of it so please don't blame and me

Did you draw the diagram? If so, you must know what the three velocities represent.
Are you sure you've left nothing out? If you haven't, why would the distance the fly travels be any different from the distance the car it is on travels?

 

[Delta31415]

My teacher drew this diagram ( it was the only thing that was on the board for hw) and the he did not say what any of the variables were,so i just said 10 so i could understand the problem better but i had no luck

 

[berkeman]

With the hints I've been giving you via PM, you really need to write out the 2 equations I suggested and start trying to solve for the time when the 2 cars meet.

 

[berkeman]

What is the equation for the distance an object travels given its velocity and the time? Include units in your equation.

Use that form of equation to write the two equations of motion for the two cars. Call it the x-axis, with the left car starting at x=0 and the right car starting at x=d.

 

[Delta31415]

average acceleration = (x-0 units/t seconds)
average acceleration= ( x-d units/t seconds)
((x-0 units/t seconds)=( x-d units/t seconds)

 

[berkeman]

average acceleration = (d units -t seconds)
average acceleration= ( 0 units - t seconds)
(d units -t seconds)=( 0 units - t seconds)

No, there is no acceleration in this problem as stated. V2 and V3 are constant until the cars meet, right?

The units of distance are meters [m]. The units of velocity are meters per second [m/s]. The units of time are seconds [ s ]

When you write an equation, the units of the lefthand side (LHS) must equal the units of the RHS. So what is the equation relating distance, velocity and time?

 

[Delta31415]

d=1/2(v2+v3)t

 

[insightful]

Could this be the following puzzle?:

Two cars with velocities v₁ and v₂ are on a straight collision course a distance d apart. A fly on one of the cars flies toward the other at velocity v₃ which is greater than either of the car's velocities. Upon reaching the other car, the fly instantly turns around and heads back toward the previous car. This repeats until the cars collide. What is the total distance the fly flies before the cars collide?

 

[Delta31415]

yes yes that is what that problem is ,but i don't know how to slove it

 

[insightful]

d=1/2(v2+v3)t

Why the 1/2?

And why the v₃ and not v₁?

 

[Delta31415]

because i don't know what i am doing and now that i look at it v1 is what fits. I got that 1/2 form this formula

 

[insightful]

OK, so what's the time before the cars collide?

 

[Delta31415]

dont know,the teacher didnt say,so do i need to know the time to slove this problem

 

[insightful]

Well, if you have two cars heading toward each other at v₁ and v₂, starting a distance d apart, how long before they collide? Not the number, the equation t = ...

 

[Delta31415]

time = distance / speed,both of which i don't know

 

[insightful]

You have the distance d. You have the closing speed v₁+v₂, so write the equation.

 

[Delta31415]

t=d/v1+v2

 

[insightful]

Excellent! So how much time does the fly have to fly?

 

[Delta31415]

dont know the values of the variables

 

[SammyS]

t=d/v1+v2

Use parentheses when needed.

 

[Delta31415]

k so t(sec)=d(m)/V1+V2(m/s)

 

[SammyS]

k so t(sec)=d(m)/V1+V2(m/s)

That says take d, divide it by v₁ , then add v₂ to that result. Is that what you mean? Use parentheses.

 

[Delta31415]

t=d/v1+v2

 

[insightful]

Please convince yourself that the fly flies the same t=d/(v1+v2).

 

[Delta31415]

k ,i know that but i don't know the vaules of the variables,so how do i solve it

 

[insightful]

You don't need values. We're going to end up with an equation.

Now that we have an equation for t, what's the distance the fly flies?

 

[Delta31415]

t x v1+v2=d

 

[insightful]

For the distance the fly flies, shouldn't you use the fly's velocity, v₃?

 

[Delta31415]

so v3=t*v1+v2

 

[insightful]

Back to basics. d=vt

 

[Delta31415]

d=vt
d=v3*d/(v1+v2)

 

[insightful]

d=vt
v3=d/(v1+v2)

Sorry, getting crossed messages.

Do you see that d, fly = v3*t?

 

[Delta31415]

yes i understand that d of fly= v3*t
Df=v3*d/(v1+v2)
equals
v1+v2*Df=v3*d
right?

 

[insightful]

v3*d/(v1+v2)
equals
v3*d=v1+v2
right?

But we already know that t=d/(v1+v2).

We have the time the fly flies = t.
We have the velocity of the fly = v3.
We know d,fly = v3*t.

So what is d,fly in terms of the given variables: d, v1,v2, and v3?

 

[Delta31415]

i edited my meassge
so reposting it
yes i understand that d of fly= v3*t
Df=v3*d/(v1+v2)
equals
v1+v2*Df=v3*d
right?

 

[insightful]

yes i understand that d of fly= v3*t
Df=v3*d/(v1+v2)
equals
v1+v2*Df=v3*d
right?

Other than parentheses around the second v1+v2, my work here is done.

Please know that this puzzle has stumped many people (usually trying to solve it with an infinite series).

 

[Delta31415]

thank you for your help

 

[Delta31415]

Now i have a new problem, my teacher wants me to solve this using with infinite series? So how do infinite series work?