1 string, 2 balls, motion problem

[thoradicus]

Homework Statement

http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_qp_41.pdf

number 6III
http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_ms_41.pdf

Homework Equations

s=ut+0.5at^2

The Attempt at a Solution

Okay, the distance of P from ground is 3m and the distance of Q from ground is 7m, already calculated. However, I am confused when the marking scheme says that the initial velocity for Q is -2m/s? why is that?

3 = 2tP + 5tP^2 initially i wrote this
7=2t+5t^2 for Q, the problem is why is the intial velocity is -2?

 

[mishek]

P & Q are moving in different directions? If one has a "positive" velocity, what will the other have?

 

[thoradicus]

But since the string breaks, the balls should all be moving downwards, right?

 

[HallsofIvy]

Homework Statement

http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_qp_41.pdf

number 6III
http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_ms_41.pdf

Homework Equations

s=ut+0.5at^2

The Attempt at a Solution

Okay, the distance of P from ground is 3m and the distance of Q from ground is 7m, already calculated. However, I am confused when the marking scheme says that the initial velocity for Q is -2m/s? why is that?

3 = 2tP + 5tP^2 initially i wrote this
7=2t+5t^2 for Q, the problem is why is the intial velocity is -2?

It doesn't. I will admit that the answer as shown is ambiguous. The problem asked for two speeds and only the speed of P is given. The speed of P (not "initial" but at the time the string broke) is -2 m/s (downward) so the speed of Q is 2 m/s (upward).

 

[thoradicus]

Ok, but why is speed of Q taken as -2, though? A bit confused. Can elaborate more?

 

[mishek]

But since the string breaks, the balls should all be moving downwards, right?

Yes, but you are asked to find the speed of the particles when the string brakes.

Before string brakes, the particles are moving. P goes down (it's heavier) and Q goes up. When the string breaks, then they both go down.

I've attached a photo. Position 1 is at rest, position 2 before string breaking and position 3 after breaking.

 

[mishek]

Ok, but why is speed of Q taken as -2, though? A bit confused. Can elaborate more?

If you mean why did they put -2 at (iii), it's because the initial velocity has different direction than the path s. The direction of the path goes from up to down. For particle P it's +2 because the initial velocity (2 m/s) has the same direction as s.

 

[thoradicus]

Ah that explains it!. thanks all much appreciated