# Homework Help: Evaluate Magnitude of Gravitation at the Surface of a Planet

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1. Sep 19, 2015

### ScrubTier

1. The trajectory of a rock thrown from a height with an initial speed of 20.9 m/s is shown in the figure below. Evaluate the magnitude of the gravitational field at the surface of the planet. The planet has no atmosphere.
https://s2.lite.msu.edu/cgi-bin/plot.png?file=muiblack_msu_1442688985_1543723_plot.data [Broken]

2. Relevant equations

Xmax=Vo^2/a*sin2Theta=Vo^2/a*2sinTheta*cosTheta

3. The attempt at a solution

Rise = 15 Run=20
Tan(x)=15/20
x=36.869 I think. I got this number but plugging this back in is not working for me. I thought I would take this and plug it into a triangle where h=20.9 (Vo) then the y-component would be the answer. This is not working.

Last edited by a moderator: May 7, 2017
2. Sep 19, 2015

### SteamKing

Staff Emeritus
What is x supposed to be? What units does it have? What does "evaluate the magnitude of the gravitational field" mean to you?

Last edited by a moderator: May 7, 2017
3. Sep 19, 2015

### ScrubTier

x is supposed to be the angle at which the rock is first thrown. It would be degrees. The magnitude of the gravitational field would be the constant y-component whereever the rock is on the graph.

4. Sep 19, 2015

### SteamKing

Staff Emeritus
No, I don't think so. According to the graph of the trajectory, there is no constant y-component. It keeps changing ...

Since this is a planet which is presumably not earth, I think the "magnitude of the gravitational field" means finding the value of g for this planet.

5. Sep 19, 2015

### ScrubTier

But how would I do that then? I'm so lost.

6. Sep 19, 2015

### SteamKing

Staff Emeritus
Write out the equations for projectile motion under a constant gravitational acceleration. You'll use the information from the graph of the trajectory to help you solve for the value of g for this planet.

7. Sep 19, 2015

### ScrubTier

Is it like the equation I included?

8. Sep 19, 2015

### haruspex

No.
The usual SUVAT equations allow you to write out the horizontal and vertical displacements as functions of time. But your graph says nothing about time. It shows a trajectory, i.e. the relationship between x and y. If you have an equation showing how x depends on t, and another showing how y depends on t, how would you obtain an equation that shows how y depends on x?

That said, there is a way to use the equation you posted. First, you have to understand what exactly xmax refers to in that equation and read that off the graph. You also need to ead theta from the graph, but it will be hard to do that with any accuracy. So I recommend working with the SUVAT equations as I described above.

9. Sep 19, 2015

### ScrubTier

Would I need Xmax and Ymax to use those equations? My professor said we should be able to read those from the graph but it isn't so clear..

10. Sep 19, 2015

### ScrubTier

What I have figured out is that I can find the x-component of Velocity by my given velocity (20.9) times cos(Launch angle) and my y-component by 20.9*sin(launch angle) but how do I find the launch angle? Can I use an angle found on the downslope?

11. Sep 19, 2015

### SteamKing

Staff Emeritus
It's not clear what you mean by "downslope" here.

Since you are given a plot of its trajectory, you can find (or approximate) the angle which the projectile takes when it is launched.

12. Sep 19, 2015

### ScrubTier

I don't understand how to do that.

13. Sep 19, 2015

### SteamKing

Staff Emeritus
Well, take the sketch and try to draw a tangent to the curve at the start of the trajectory. The angle this tangent line makes to the horizontal will be launch angle, or a close approximation.

14. Sep 19, 2015

### ScrubTier

I know how to find the angle I just don't know what measurements to use. Would x=0, 20 y=15, 30 be close enough?

15. Sep 19, 2015

### ScrubTier

I just tried by using those numbers. It was wrong. I know I must use something to find the Launch Angle then find x-component of velocity and y-component of velocity. Then determine the Xmax (distance which it traveled when it made it back to the starting height (15m)) and Ymax (max height it got to). I use these in d(Xmax)=Vo(x)*t to find t then d (which is 0) = Vo(y)*t-1/2*g*t^2
I just do not know what numbers to use to find these things!!

16. Sep 19, 2015

### SteamKing

Staff Emeritus

17. Sep 19, 2015

### ScrubTier

If you look at the picture of the graph finding coordinates to do calculations with is very un-exact. That is my problem.

18. Sep 19, 2015

### SteamKing

Staff Emeritus
Yes, I understand that.

But what are we to suggest to you in response to the statement, "I got it wrong"?

19. Sep 19, 2015

### ScrubTier

I really want advice as to what numbers I should use for my equations. Estimates to what Xmax should be would be helpful.

20. Sep 20, 2015

### haruspex

That looks somewhat off to me. As I posted, I think that estimating the launch angle directly from the graph is a rather inaccurate way to proceed. You would be much better off picking a point on the trajectory that is clear (max height gain and x at that point) and finding the gravitational acceleration and angle which hit it.