Need help with the sign of g in free fall acceleration

In summary, the time elapsed between the first splash and the second splash is 4.08 seconds. To solve for this, we use the equations s=ut+\frac{1}{2}at^2 and t_{B}-t_{A}=t_{elapsed}, with positive g for Heather's rock and negative g for Jerry's rock. This results in two quadratic equations that can be solved for t, giving us the time elapsed.
  • #1
hachi_roku
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Homework Statement


Heather and Jerry are standing on a bridge 50\;m above a river. Heather throws a rock straight down with a speed of 20\;m/s. Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance.

How much time elapses between the first splash and the second splash?
4.08 s


Homework Equations





The Attempt at a Solution



i already have the answer of 4.08 s, which according to mastering physics, is correct.

question is: in solving the equations i was instructed to use a positive g for heather and a negative g for jerry...i don't get this.

maybe i did the problem wrong and got the correct answer.
 
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  • #2
This question will use the equation:
[tex]s=ut+\frac{1}{2}at^2[/tex]
where:
s=displacement
u=intial velocity
a=acceleration due to gravity
t=time elapsed

If we label Heather's stone as A, and Jerry's as B, then [tex]t_{B}-t_{A}=t_{elapsed}[/tex]

If we substitute all our known results into the formula for stone A, we get:

[tex]50=20t+\frac{1}{2}gt^2[/tex] (g=gravity)

notice how all values are positive, because the displacement is downwards, the velocity of the rock is directed downwards, and the gravity is acting downwards. Similarly, all values could be negative in the equation if we take up to be the positive.

Now all you have is a quadratic equation in t.

For rock B, we get:

[tex]50=-20t+\frac{1}{2}gt^2[/tex]

notice how the only difference now is that the initial velocity is negative, since the rock is being thrown upwards, or away from the displacement and gravity direction.
Solve this for t as well and you can then find your difference. If you are hopeful you know what you're doing, I suggest when using the quadratic formula (or any other method to solve for t) that you leave g as a variable, and once you get your answer in terms of g, then substitute the 9.8ms-2.
 
  • #3



In free fall acceleration, the acceleration due to gravity is always directed downwards, towards the center of the Earth. This acceleration is represented by the symbol g and it is always a negative value. This is because the direction of acceleration is opposite to the direction of motion.

In this problem, both Heather and Jerry are experiencing the same acceleration due to gravity, but in opposite directions. Heather is throwing the rock downwards, so her acceleration is positive and Jerry is throwing the rock upwards, so his acceleration is negative.

When solving equations for free fall acceleration, it is important to use the correct sign for g depending on the direction of motion. In this case, Heather's equation would have a positive g and Jerry's equation would have a negative g.

Therefore, using a positive g for Heather and a negative g for Jerry is the correct approach for solving this problem. It is possible that you may have arrived at the correct answer using a different approach, but using the correct signs for g is important in accurately representing the physics of the situation.
 

1. What is the sign of g in free fall acceleration?

The sign of g in free fall acceleration is always negative, indicating the direction of acceleration due to gravity towards the center of the Earth. This means that an object in free fall will accelerate downwards towards the ground.

2. Why is the sign of g in free fall acceleration negative?

The sign of g in free fall acceleration is negative because it represents the direction of acceleration due to gravity, which always points towards the center of the Earth. This means that an object in free fall will accelerate downwards towards the ground.

3. Can the sign of g in free fall acceleration ever be positive?

No, the sign of g in free fall acceleration is always negative. This is because the acceleration due to gravity always points towards the center of the Earth, regardless of the direction of the object's motion.

4. How does the sign of g in free fall acceleration affect the motion of an object?

The sign of g in free fall acceleration determines the direction in which an object will accelerate. If the sign is negative, the object will accelerate downwards towards the ground. If the sign is positive, the object will accelerate upwards away from the ground.

5. Is the sign of g in free fall acceleration the same for all objects?

Yes, the sign of g in free fall acceleration is the same for all objects. This is because all objects experience the same acceleration due to gravity on Earth, regardless of their mass or size.

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