Confusion over acceleration of gravity as positive/negative

[helloworld2941]

Homework Statement

A skateboarder jumps horizontally off the top of a stairs and lands at bottom of the stairs. The staircase has a horizontal length of 12m, and the jump lasts 1.10s. We can ignore air resistance.

Relevant Equations

V = u + at

okay I annotated the diagram given and the grey thing where they take y axis up as positive is what I understand to be, right?

But in the answers, they start off by going V = u - gt. They've taken acceleration due to gravity as a negative value. Why? I thought the skateboarder was falling downwards, and gravity acts downwards, so shouldn't it be positive?

Because I have understood that in other questions where upwards is positive and it'll ask something like a ball is projected upwards, that's when gravity is negative? Or did I confuse the the sign conventions and in those questions they actually took downwards as positive?

I am so confused. The answer is 10.78ms^-1 down which I would get the magnitude but have messed up the sign because my first instinct was to have acceleration due to gravity as positive, V = u + gt before subbing values.

Thank you so much

 

[haruspex]

The diagram indicates that upward displacements are positive. To avoid confusion, it helps then to make upward velocities and accelerations positive.
By convention "g" is a magnitude, so positive.
Since gravitational acceleration is downwards, and we are taking upward acceleration as positive, the acceleration due to gravity must be negative, so -g.
v=u+at=u-gt.

 

[helloworld2941]

The diagram indicates that upward displacements are positive. To avoid confusion, it helps then to make upward velocities and accelerations positive.
By convention "g" is a magnitude, so positive.
Since gravitational acceleration is downwards, and we are taking upward acceleration as positive, the acceleration due to gravity must be negative, so -g.
v=u+at=u-gt.

Thank you, I understand it for this question now. But then in scenarios where a ball is projected upwards, would the acceleration due to gravity be positive or negative?

 

[phinds]

Thank you, I understand it for this question now. But then in scenarios where a ball is projected upwards, would the acceleration due to gravity be positive or negative?

If you throw a ball upwards and the acceleration due to gravity is positive, then the ball will accelerate starting at the initial velocity and just go on up forever.

 

[haruspex]

Thank you, I understand it for this question now. But then in scenarios where a ball is projected upwards, would the acceleration due to gravity be positive or negative?

Necessarily falling is in the direction of gravity. You can choose whether to represent that direction as positive or negative.
It doesn’t matter which way the ball starts moving. If it starts upwards then that velocity and gravity will have opposite signs. Consequently the magnitude of the velocity decreases at first, as you would expect.

 

[helloworld2941]

If you throw a ball upwards and the acceleration due to gravity is positive, then the ball will accelerate starting at the initial velocity and just go on up forever.

Wait that's such a good way of thinking about. I've never learnt of it like that

 

[PeroK]

Thank you, I understand it for this question now. But then in scenarios where a ball is projected upwards, would the acceleration due to gravity be positive or negative?

It's up to you, as part of setting up the solution to a problem, to decide which direction is positive. Unless the problem statement already includes this decision.

Suppose a car is moving along the road from left to right. To someone facing you on the the opposite side of the road the car is moving from right to left. If you both use the convention that the positive x-axis goes from left to right, then you would naturally give the car a positive velocity and the other observer would give the car a negative velocity. Both represent the same physical scenario.

 

[Lnewqban]

@helloworld2941
What is the problem asking for?
What V and u means to you?
Should the horizontal and vertical components of the initial velocity change with time?
If so, how and why?

 

[DaveC426913]

Thank you, I understand it for this question now. But then in scenarios where a ball is projected upwards, would the acceleration due to gravity be positive or negative?

This is important: The reason you are being assigned these questions is much more than just doing the calculations by rote; what you are learning is to understand and interpret what the question is asking, and how to correctly determine such things as variables and signs.

 

[phinds]

This is important: The reason you are being assigned these questions is much more than just doing the calculations by rote; what you are learning is to understand and interpret what the question is asking, and how to correctly determine such things as variables and signs.

Which is why, post #4

 

[DaveC426913]

Which is why, post #4

Yes. I felt it was worth repeating. In principle, such understanding is a more important lesson than doing the math.