M1 Question - help please

Question 6(c)
Question 5(b)

Can somebody explain what i have to do when the term 'taut' is used in questions like these?

for 5(b) I worked out the initial velocity (which is final velocity of B- i think) and used a = - 9.8g and v = 0 to work out the s value using v^2=u^2 + 2as

I got the answer 0.3m but in the mark scheme it's 0.6m (0.3m x 2) I think it has something to do with the term taut but i don't know.

For 6(c) I'm just completely lost, i was able to answer (a) and (b) correctly but i have no idea how to answer (c).

Can somebody explain what i have to do in both of these questions that use the term taut in them?

Any help is greatly appreciated, thanks!

6(c) Taut just means the tension in the string/ropes are >0. Slack means the tension is 0. So probably you're meant to find T in terms of k and then set T > 0. Remember there are two different ropes though and they're both non-zero tension (i.e: taut).

I think in part (b) you find that $T_B = W(2-3k)/6$, so in part (c) you need only solve $T_B \geq 0$ to find the set of values for k.

5(b) - you found s = 0.3, sure, that's the height of the string, but in this motion, the string is limp - surely you can visualise this, it flies upwards and it's just limp and hence slack, i.e: no tension - it first becomes taut (regains tension) when it falls to its initial height. i.e: moves up 0.3 and then moves down 0.3 for a total of 0.6 metres.

Thank you so much!