Need help with a M1 hard question

can anyone please explain why the downward direction is negative in part c ? Why isn't it positive? Thanks.

You can take down as positive if you like. If you do, s and a will be positive but u will be negative since it is upwards. The equation will turn out the same.

Why do you think this question is hard (this is a genuine question, not someone getting at you)? Is it because there are lots of letters in the answers, rather than numbers?

Firstly thanks for helping. U would just be 0 so as it goes from the top all the way down. How does this work? I am using +4H as the height. So a would also be g I get that. So I am not sure about u that u are talking about. The fact that I have to substitute Tg into u is confusing. Depends on how advanced you are though, obviously a further maths person and a maths student at uni will find this easy. Thanks. Also by saying it's hard will get more help as people who are helping would of course be more knowledgeable than I am.

Remember that your starting point is 3H metres from the ground. So it starts from middle then goes up then goes below middle to the ground.

u is your initial speed and is hence Tg (from part (a)).
s is your displacement and is -3H since you're taking upwards as positive and the ball starts from a height of 3H above the ground and ends up on the ground so it has a total displacement of 3H downwards. But upwards is positive so s = -3H.
Remember what displacement is. If I move 2 metres forwards and then 2 metres backwards, that's a displacement of 0 metres and a distance of 4 metres.
So you launch your ball from A which is 3H metres above the ground and then it flies up to its maximum height but then it falls back down to the ground, the total displacement is just -3H metres.
a is your acceleration and is -g here. That's because gravity acts downwards and you're taking upwards as positive.

That's pretty much it, what specific part is confusing you?

Oh yeah, that's like a standard question isn't it. I didn't remember that as this involves the substitution of T and ug and this just makes everything so chaotic. Never mind, thanks.

Oh yeah, that's like a standard question isn't it. I didn't remember that as this involves the substitution of T and ug and this just makes everything so chaotic. Never mind, thanks.

So this sounds as though the use of letters rather than numbers is what made this question hard for you, compared with other questions on the same topic. That's what I was trying to find out.

Is this something you've noticed whilst marking papers, as in - do candidates tend to perform, on average, worse when dealing with algebraic quantities over numerical?