Exploring Projectile Motion in Reduced Gravity: Calculating Football Distance

[Lori]

Homework Statement

A student can throw a football a max range of 60 meters. How far could he throw it if the Earth's gravity were reducted to 1/6 of its normal value , similar to the moon's gravity?

Homework Equations

v = .5at^2

The Attempt at a Solution

I feel like i did this wrong but

x = .5at^2
60 = .5(9.81)t^2
t= 3.5
x = .5((1/6)9.81)*3.5^2
x=10 m

 

[phinds]

1) Your attached file has nothing to do with your post
2) Yeah, I'd sure guess you did SOMETHING wrong since you have the ball going 60 meters on the Earth and only 10 on the moon, which clearly is just silly.

 

[Lori]

1) Your attached file has nothing to do with your post
2) Yeah, I'd sure guess you did SOMETHING wrong since you have the ball going 60 meters on the Earth and only 10 on the moon, which clearly is just silly.

Would the range still be 60m then because forces in the y direction don't affect x?

 

[phinds]

Would the range still be 60m then because forces in the y direction don't affect x?

How can you think that? If you throw a baseball you can probably get it to go, say, 100 feet. Do you think you could do the same with a 20lb tossing weight if you give it the same force in the x direction? The only difference will be the force in the y direction.

 

[Lori]

How can you think that? If you throw a baseball you can probably get it to go, say, 100 feet. Do you think you could do the same with a 20lb tossing weight if you give it the same force in the x direction? The only difference will be the force in the y direction.

I see. I do understand that the ball would probably travel farther since gravity pulling down at it is smaller. Am I using the wrong equation?

 

[CWatters]

You calculated a time and then assumed the time would be the same in both cases. Why?

 

[Lori]

You calculated a time and then assumed the time would be the same in both cases. Why?

oh right. The kinematic equation i use assume that acceleration is constant . But, it's not here

 

[Lori]

Let me think about this again...

d = .5at^2
d = .5(1/6a)t^2
d/(1/6) = .5at^2
6*d = .5at^2

So , 6*d means that distance is multiplied by 6 , so 360 meters?

 

[Ray Vickson]

oh right. The kinematic equation i use assume that acceleration is constant . But, it's not here

The acceleration due to gravity is not constant? Why do you claim that?

Of course, for footballs that go 1000 miles up, the acceleration is probably detectively non-constant over the whole trajectory, but for ordinary footballs thrown at ordinary height (or even 100 times ordinary height) you would probably not be able to measure the non-constancy of $g$. (Air resistance would be a much, much more important factor, but I presume we are neglecting that.)

 

[CWatters]

Perhaps make a list of all the factors that determine how far an object will go when thrown. Then decide which are likely to be the same in both cases. Forget equation for the moment.

 

[I like Serena]

Hey Lori!

You seem to assume that the horizontal motion is accelerated by gravity.
But it isn't, is it?
Isn't it the vertical upward motion that is decelerated by gravity?

Note that we get the furthest throw (when neglecting friction by air), if we angle the throw by 45 degrees.