Projectile motion homework help

[nirvana1990]

Why is gravity always taken as negaive when applied to the whole projectile i.e. when finding the time of flight for the entire projectile we use gravity as -9.8 even though it is only negative for the first half of the projectile while the object is moving upwards against gravity?
Please help as i am very confused!

:uhh:

 

[Kurdt]

Its just a convention. Positive speed and positive acceleration tell us that it is directed upwards whereas negative speed and negative acceleration indicate a downward motion. it would work just as well the other way around if a little counter intuitive.

 

[neutrino]

Welcome to PF!

when finding the time of flight for the entire projectile we use gravity as -9.8 even though it is only negative for the first half of the projectile while the object is moving upwards against gravity?

I'm not sure what you mean by that.

Remember Newton's second law? It says that direction of the force and acceleration are the same. At all times during the motion of the projectile the direction of the force of gravity (we assume a uniform gravitational field) always points down, towards the ground. Also, for convenience, we usually set up the coordinate system such that the negative y-axis points in this direction. Therefore the gravitational force, $F_g = -mg\hat{y}$.

 

[nirvana1990]

Right...but since gravity always acts downwards, the acceleration for the 1st half of the projectile motion should be -9.81 since the object is decelerating towards its max. height but the acceleration for the downwards projectile motion (e.g.when the ball is on it's way back down to earth) should be +9.81 since the ball is accelerating. So when calculating the time of flight using S=Ut+0.5at^2 applied to the vertical motion only why do we use a as -9.81 even though a should only be negative while the ball is going upwards?
I hope this is understandable! i have a way with words!

 

[Kurdt]

The acceleration is always downwards. In the coordinate system that is conventional downwards is represented by a negative sign. The sign doesn't change once the projectile starts falling to Earth.

I think you are confusing a negative sign to mean deceleration and a positive to mean acceleration and that is just not the case. The sign indicates the direction of the acceleration.

 

[neutrino]

So when calculating the time of flight using S=Ut+0.5at^2 applied to the vertical motion only why do we use a as -9.81 even though a should only be negative while the ball is going upwards?

For a body accelerating towards the ground, the equation would actually read,

$$s = h_{max} + ut + \frac{1}{2}at^2$$

u = 0, therefore $s - h_{max} = \frac{1}{2}at^2$. Is $s - h_{max}$ positive or negative?

 

[nirvana1990]

Oh i see, i'd never have thought of it like that! Thank you soo much! I can now rest!

 

[neutrino]

I think you are confusing a negative sign to mean deceleration and a positive to mean acceleration and that is just not the case. The sign indicates the direction of the acceleration.

That's true. When the direction of the velocity and acceleration are opposite, then the body is slowing down, or decelerating.