How Does Time Relate to Distance in Gravity Experiments?

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The discussion focuses on creating a graph to illustrate the relationship between distance (s) and time squared (t²) based on the equation s = (1/2)gt², with a constant distance of 0.8m. Participants are asked to plot values of time (t) provided as 0.36s, 0.40s, 0.44s, 0.38s, 0.48s, and 0.40s. The equation can be rearranged to derive g using the formula g = (2s)/t². The user mentions using a graphing tool, Autograph, to visualize the data but seeks further explanation on the graph's interpretation. The discussion emphasizes understanding the mathematical relationship between time and distance in gravity experiments.
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Homework Statement


Draw a graph showing the relationsip between 2s and t2 (derived from the equation
s=\frac{1}{2}gt2

g=\frac{2s}{t^2}

You are given six different values for t i.e
0.36s
0.40s
0.44s
0.38s
0.48s
0.40s

In all instances the value for s=0.8m

Homework Equations


No restriction


The Attempt at a Solution


I used autograph and my graph looks something like this.
 

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We can't see the graph yet but maybe you could explain what you've done.

The Bob
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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