TBR, Physics, Trans. Motion, #29

[Sammy1024]

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29. Suppose that while a kicked football is in flight due north through the air, a crosswind is blowing from the east to the west is blowing. This causes the x-direction displacement of the football to:

A. increase.
B. decrease.
C. remain the same.
D. We need to know the magnitude of the crosswind before we can answer this.

The answer is C, but I picked B. I was thinking that if it were to travel lets say 5 m in the x direction and the wind is blowing perpendicular, the trajectory would be altered and it would travel less?

Something like the lines above. They're the exact same length line, but one is at an angle because the crosswinds were blowing at it.

Can someone explain why C is the answer?

 

[el_duderino]

I'm not sure what they mean by "x-direction displacement." The question talks bout cardinal directions. Which axis is "x"?

 

[Sammy1024]

The passage is about kicking a football past the goal posts, and what I inferred is that if you look at the side view, x is the horizontal direction of the football, and y is the vertical/height of the football.

The crosswinds would be coming towards you.

 

[Cawolf]

I don't know if that included a picture - but I would generally assume that the x axis is east/west, y axis is north/south, and z axis is up/down.

Therefore here the ball is traveling with some velocity in the +y direction towards the goal and the z direction up then down as is falls.

There is no initial x velocity. When the wind pushes it west - there is a force acting in the -x direction, so the ball will gain some x velocity.

The total distance traveled in only based on time for the ball to fall, or it's z velocity.

So changing the x velocity will alter it's path, but not the time it travels - making C the correct answer.

 

[Sammy1024]

This is what the answer said:

I dont understand why the z direction would have no effect on the x direction. If a ball is going to travel 5 m in 10 s of flight, and the angle of the flight is now changed, and it will be going 5 m in 10 s at an angle of 20°, it shouldn't be going just as far?

 

[el_duderino]

So if the x-axis is the horizontal axis along which the ball is traveling, a cross wind will not affect time in flight or x velocity, and therefore not affect x displacement.

The ball will end up further from the spot it was kicked, because it will have the same x displacement and then some additional y displacement which would be zero before.

The only way I can arrive at that explanation is if I already know the answer. X could just as easily be east/west as north/south, in which case the answer would be A.

 

[Sammy1024]

I guess it's a bad question? TBR is so confusing sometimes.

 

[Cawolf]

Oh ok so they said it is traveling in the x/y forward/up direction and the wind blows in the z direction.

The angle you are describing is effecting the left/right motion of the ball. So the force forward from the kick is not changed, but some constant force is accelerating the ball to your left. The forward travel will not be changed by adding a leftward component, the new path would be the hypotenuse of the triangle formed with the legs being the forward and leftward paths. So the ball will travel farther overall, but the forward leg is still the same.

If I could draw it for you I would - sorry.

 

[el_duderino]

This is what the answer said:

View attachment 183510

I dont understand why the z direction would have no effect on the x direction. If a ball is going to travel 5 m in 10 s of flight, and the angle of the flight is now changed, and it will be going 5 m in 10 s at an angle of 20°, it shouldn't be going just as far?

A crosswind would increase the speed of the ball. It would have the same speed in the north-south direction, but the crosswind would add east-west speed, thus increasing the magnitude of the velocity. It's not like the ball is going 20 m/s forward with no crosswind and 20 m/s at some angle to forward with the crosswind.

If it's going 20 m/s forward and you add a horizontal crosswind, it will continue going 20 m/s forward but also 3 m/s (or whatever) sideways for a total of 20.22 m/s velocity. Time in flight stays the same and forward velocity stays the same.

 

[el_duderino]

I guess it's a bad question? TBR is so confusing sometimes.

Yes. The non-AAMC books/question banks have a lot of pretty bad questions. I don't like them for that reason.

 

[Sammy1024]

The angle you are describing is effecting the left/right motion of the ball. So the force forward from the kick is not changed, but some constant force is accelerating the ball to your left. The forward travel will not be changed by adding a leftward component, the new path would be the hypotenuse of the triangle formed with the legs being the forward and leftward paths. So the ball will travel farther overall, but the forward leg is still the same.

The angle I drew was if I was looking down at the ball from above.

Sorry this is so confusing!

 

[Cawolf]

Oh ok - in your original picture that leg would not shorten.

 

[el_duderino]

This is what the answer said:

View attachment 183510

I dont understand why the z direction would have no effect on the x direction. If a ball is going to travel 5 m in 10 s of flight, and the angle of the flight is now changed, and it will be going 5 m in 10 s at an angle of 20°, it shouldn't be going just as far?

Why would a force in the Z-direction have any effect on motion in the X-direction?

 

[DrknoSDN]

I dont understand why the z direction would have no effect on the x direction. If a ball is going to travel 5 m in 10 s of flight, and the angle of the flight is now changed, and it will be going 5 m in 10 s at an angle of 20°, it shouldn't be going just as far?

Your thinking that the initial angle is being altered. That is not the case here.
If the original launch angle of the football was altered then yes it would not travel as far in the X direction.

Here the wind is adding additional force in the Z direction after a full kick of force was already applied in the X direction. Once the football is in the air after being kicked full force in direction X, the only thing that could alter the distance is a shorter flight time, or a force in the X or -X direction.

The wind is effectively increasing the "speed" of the ball during the flight to get the Z-translation but X "velocity" is not altered.