# Projectile motion homework help

1. May 28, 2007

### 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?

:uhh:

2. May 28, 2007

### Kurdt

Staff Emeritus
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 aswell the other way around if a little counter intuitive.

3. May 28, 2007

### neutrino

Welcome to PF!

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, $F_g = -mg\hat{y}$.

4. May 28, 2007

### 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!

5. May 28, 2007

### Kurdt

Staff Emeritus
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.

6. May 28, 2007

### neutrino

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?

Last edited: May 28, 2007
7. May 28, 2007

### nirvana1990

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

8. May 28, 2007

### neutrino

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