In what cases do you use -9.8m/seconds squared?

Question

With projectile motion, my teacher has switched from positive 9.8 to negative..But then when..
A golf ball rolls off a horizontal cliff with an initial velocity of 11.4m/s. The ball falls a vertical distance of 15.5M into a lake below. (a) How much time does the ball spend in the air? (b) What's the velocity of the ball just before it strikes the water?

Using Final Velocity=Square root[Initial velocity squared+2acceleration*displacement..

He uses positive 9.8...

..
Before, when asking us like "How far will a ball go if thrown with an initial velocity of 7m/s? We used positive 9.8

Now with projectiles, he's saying negative 9.8 for projectiles, but in this case, uses positive so that it fits in the square root? Your right though, my teacher sucks.

Answer 1

When forces oppose one another, one will be positive and the other negative. You need to decide which will be positive and negative.
Going up, is usually positive, and going down (gravity) is usually negative.
The situation of the golf ball, putting it simply, it's that only one vertical force is acting on it and so you don't need to distinguish between positive and negative.

The fact that the ball rolls off a horizontal cliff has no bearing on the downward velocity, only how far the ball will be out from the cliff. This implies the initial velocity will be zero m/s.

u - initial velocity.
v - final velocity.
t - time taken.
s - distance.
a - acceleration (due to gravity).

v² = u² + 2as
v² = 0² + 2(9∙81..)(15∙5)
v² = 304∙11
v = √304∙11
v = 17∙438 749 96
v ≈ 17∙439 m/s.


v = u + at
v - u = at
t = (v - u) / a
t = (17∙438 749 96 - 0) / 9∙81
t = 1∙777 650 352
t ≈ 1∙778 sec.

Answer 2

9.8 m/s^2 is acceleration toward the ground. What sign you use depends on what direction you are considering positive in the particular problem you are doing. I think most projectile problems consider up as the positive direction, in which case you would use negative 9.8. For the falling body, it would hit the ground at a negative velocity. Negative 10 meters per second is a speed of 10 in the down direction. A velocity of positive 10 meters per second would be a speed of 10 in the up direction. Notice that in these two cases speed is the same but velocity is not.

Answer 3

Good question.

In the case of the golf ball as a projecticle, the ball is moving up and in the direction opposite the force of gravity; therefore we use -9.8m/s^2.

In the case of the golf ball rolling off a cliff, the ball is falling down and in the direction of the force of gravity;
therefore we use +9.8m/s^2.

Don't be ashamed to ask your teacher. I'm sure he'd gladly give the answer.

Answer 4

a ball cant have an initial velocity rolling horizontal...that is another application, no wonder you are confuzed, the teacher knows not what he/she is asking!