confused over man catching a bus

[apple2357]

I am a little confused by this question (14 below) and the solution





In my attempt, i had assumed that when the man catches the bus, the speed of the bus and the man needs to be the same. I am now questioning it.. can someone clarify for me please?

 

[apple2357]

Is there a better way to approach this without making this assumption?

 

[Steven G]

Why would you think that the speeds have to be the same. Suppose the bus is traveling around 30mph (I say around since it is accelerating) and you are one step (instead of 50m) from the bus stop> Do you really have to make that last as quickly as the bus.

 

[Steven G]

The more I read this problem the more I get confused. Where does the man catch the bus? Usually buses only pick up passengers at a bus stop, not when someone catches up to them in the middle of the street. Are the bus and man running in the same direction, opposite direction or something else? That is what angle is the man running at (if the man is running in a straight line--we do not know) with respect to the direction the bus is traveling (if in fact the bus is going straight). Initially the bus is stopped at a bus stop and then accelerate away. So are we saying that when the man catches up to the bus (if they are going in opposite direction) that the bus hits the man? Or maybe the man jumps onto the back of the bus or do we assume that when the man catches up to the bus the stops dead cold.

I have been on this website for over five years and unless I am missing something this has to be the worst posed question I've seen so far. Who writes these problem?!

 

[Steven G]

I read the problem again and noticed that it does not say how fast the man is running nor the acceleration of the bus. So I claim that there are an infinite number of solutions!

Assuming the man and bus are heading towards one another: Suppose the man runs very slowly towards the bus and the distance that the man goes in 30s is 2m. There IS a constant acceleration that the bus can leave the stop at to travel 48m in 30s.

If the man runs a little faster, then maybe he will have traveled 5m in 30s. Again, there is an acceleration that the bus can use so that the bus travels 45m in 30 seconds. ......

 

[Steven G]

Is there a better way to approach this without making this assumption?

Yes, don't bother doing this problem as it is as flawed as can be!

 

[lev888]

The more I read this problem the more I get confused. Where does the man catch the bus? Usually buses only pick up passengers at a bus stop, not when someone catches up to them in the middle of the street. Are the bus and man running in the same direction, opposite direction or something else? That is what angle is the man running at (if the man is running in a straight line--we do not know) with respect to the direction the bus is traveling (if in fact the bus is going straight). Initially the bus is stopped at a bus stop and then accelerate away. So are we saying that when the man catches up to the bus (if they are going in opposite direction) that the bus hits the man? Or maybe the man jumps onto the back of the bus or do we assume that when the man catches up to the bus the stops dead cold.

I have been on this website for over five years and unless I am missing something this has to be the worst posed question I've seen so far. Who writes these problem?!

I don't know, it seems clear to me.
1. The bus stop is 50m away when the bus and the man start moving.
2. They move in the same direction (otherwise the whole catching thing doesn't make sense)
3. The man and the bus are points. The man "catches" the bus when the 2 points are at the same location.
4. I'm guessing their speeds should be the same at that moment, since the man _just_ catches the bus. Not sure though.

 

[Steven G]

I don't know, it seems clear to me.
1. The bus stop is 50m away when the bus and the man start moving.
2. They move in the same direction (otherwise the whole catching thing doesn't make sense)
3. The man and the bus are points. The man "catches" the bus when the 2 points are at the same location.
4. I'm guessing their speeds should be the same at that moment, since the man _just_ catches the bus. Not sure though.

Do you think that I am wrong in post#5?

 

[lev888]

Do you think that I am wrong in post#5?

I disagree with heading towards one another - infinitely many solutions and not compatible with just catching the bus.

 

[Steven G]

I disagree with heading towards one another - infinitely many solutions and not compatible with just catching the bus.

Ok, so the bus and man are moving in the same direction. The problem makes sense in that scenario. Thanks for pointing it out.

 

[apple2357]

I don't know, it seems clear to me.
1. The bus stop is 50m away when the bus and the man start moving.
2. They move in the same direction (otherwise the whole catching thing doesn't make sense)
3. The man and the bus are points. The man "catches" the bus when the 2 points are at the same location.
4. I'm guessing their speeds should be the same at that moment, since the man _just_ catches the bus. Not sure though.

I am glad you are still not sure, i thought it was just me. Another way i was looking at it was the displacement of the bus can be described using a quadratic ( 0.5at^2) but for the man it will be linear ( ut+ 50), is this a case of the line being a tangent to the quadratic ( at some point) and therefore the speeds are the same. A different speed and the line would not intersect with the quadratic at all ( he doesn't catch the bus). I am not sure what two intersections would mean. Still dont quite know why i can assume the same speed at that moment ( is it a minimum speed as he just catches the bus?)

 

[apple2357]

In the above i mean s_bus = 0.5at^2 + 50 and s_man= ut

 

[lev888]

I am glad you are still not sure, i thought it was just me. Another way i was looking at it was the displacement of the bus can be described using a quadratic ( 0.5at^2) but for the man it will be linear ( ut+ 50), is this a case of the line being a tangent to the quadratic ( at some point) and therefore the speeds are the same. A different speed and the line would not intersect with the quadratic at all ( he doesn't catch the bus). I am not sure what two intersections would mean. Still dont quite know why i can assume the same speed at that moment ( is it a minimum speed as he just catches the bus?)

Yes, I think it's tangent, not at some point, but at the point where they meet - 30sec.
Yes, it's the minimum speed.