The acceleration due to gravity on the Earth is negative, why is the accel. due to g on the moon Positive?

Question

My teacher gave me a problem saying "The acceleration due to gravity on the surface of the moon is 1.62 m/s^2. If you can throw a ball straight up to a height of 25 m on Earth, how high would it reach on the Moon when launched at the same velocity?"

It's the problem itself that I have a question with :
I know acceleration due to gravity on Earth is -9.81
The problem states the Moon's a. due to g. is 1.62.

Is this a typo or is the Moon's acceleration really positive?? I don't understand!

Answer 1

Whether on Earth or Moon or any other planet, acceleration due to gravity will be positive when an object is falling down, and negative when the object is thrown up. In your problem, ball is thrown straight up. Hence acceleration is negative (-9.81) and on the Moon, it will be (- 1.62).



Generally, acceleration due to gravity is referred in positive. Thats why your teacher has referend Moon's gravity 1.62 in positive. Based on the nature of the problem, we have to assign either positive or negative symbol to the value.

Answer 2

Whether you use gravity, or acceleration in general, as a positive or negative value depends on whether the acceleration is, for a given object, an accelerating or decelerating force. That is, it depends on the direction of acceleration relative to the velocity.



In other words, both velocity and acceleration are vectors, which means their direction is important. Let's say you have an initial velocity going in one direction:



(Pretend these arrows are vertical)



--- velocity ---> (25 m/s up)



The you introduce an acceleration in the opposite direction:



<--- acceleration --- (9.8 m/s^2 down)



In your equations, this would be negative acceleration because the acceleration vector is the opposite direction to the velocity vector. So you can work out how long it will take the ball to reach it's peak height using the equation:



v = u + at



Initial velocity (u) = 25 m/s

Final velocity (v) = 0 m/s

acceleration (a) = g = -9.8 m/s^2 (negative acceleration, opposite direction to the velocity)



So this equation will tell you how long it takes for the ball to slow down from 25 m/s to 0. Solving for t, the equation becomes:



0 = 25 + (-9.8t)

-9.8t = -25

t = 25/9.8

= 2.55 seconds



Conversely, we can work this out in reverse by working out how long it will take for a ball falling from its peak height, with an initial velocity of 0 m/s, until it reaches a final velocity of 25 m/s. The vectors in this case look like this:



<--- final velocity --- (25 m/s down)

<--- acceleration --- (9.8 m/s^2 down)



Initial velocity (u) = 0 m/s

Final velocity (v) = 25 m/s

acceleration (a) = g = 9.8 m/s^2 (positive acceleration, same direction as the velocity)



v = a t

25 = 9.8 t

t = 25/9.8 = 2.55 seconds



So this is the time taken for one half of the ball's journey. The total flight time will be 2.55 seconds going up, then another 2.55 seconds going down.



You can now work out how high it would reach on earth using the equation



s = ut + 1/2at^2



The easiest way is to calculate this by working out how far the ball will fall in 2.55 seconds, since then the initial velocity (u) will be 0, and thus simplifies the equation to



s = 1/2at^2



I'll leave this for you to do. Solving this problem for the moon is the same, but you need to redo one of the earlier equations using the moon's gravity, rather than earth, to get the time.

Answer 3

Whenever any object falls towards any body[ here , earth and moon] acceleration due to gravity is always positive. but when we throw any object upwards, acceleration due gravity is negative. simple







hope u understood.....