How Does Reducing Earth's Gravity Affect the Time a Thrown Ball Takes to Return?

[Gear2d]

Homework Statement

If I throw a ball straight up to a height h with velocity v and it takes the ball time t to go up and back to my hands, by how much would time increase or decrease if gravity on Earth where changed from g to g/6?

Homework Equations

v = a*t

The Attempt at a Solution

I wanted make sure what I am thinking was correct. I thought about this problem as a projectile problem and said that t = (v*sin(theta))/a, where "a" is acceleration. Now since the ball was thrown straight up, I made sin(theta) to sin(90). So the problem comes out to be t=v/a, and since "a" decreases by a factor of 6 that means time increase by a factor of 6. Would this reasoning be the correct way to do it?

 

[tiny-tim]

v = a*t

Hi Gear2d!

Your reasoning and your result are right … but your initial equation is wrong.

The general equation is v₂ - v₁ = at …

so what do you think it is in this particular case?

 

[baba89]

I would say that your reasoning is generally correct. However, there are a few things to consider in this scenario. First, the equation v = a*t that you have used assumes that the initial velocity of the ball is zero. In reality, when you throw a ball straight up, it will have an initial velocity in the upward direction. This means that the equation you should use is v = u + at, where u is the initial velocity and a is the acceleration due to gravity. So, the time it takes for the ball to reach its maximum height and return to your hand would be t = (v-u)/a.

Secondly, when you change the value of g to g/6, you are also changing the value of a. In this case, a decreases by a factor of 6, which means that the ball will take longer to reach its maximum height and return to your hand. Therefore, the time will increase by a factor of 6, as you correctly stated.

Overall, your reasoning is sound and you have correctly identified the relationship between time, velocity, and gravity in this scenario. Keep up the good work!