Finding g given height & time

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To calculate the acceleration due to gravity (g) using height and fall time, the formula d = v1*t + (1/2)at^2 can be applied, where v1 is the initial velocity (0 for free fall). Given a fall time of 0.4249 seconds and a height of 1.002 meters, the equation simplifies to g = 2d/t^2. Substituting the values, g can be calculated with the appropriate significant figures, considering the uncertainties in measurements. This approach provides a method to derive the value of g accurately for the physics lab assignment.
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Calculating "g" given height & time

This problem is part of a physics lab. I need this step to finish the other parts of the lab, and I can't figure out how to do this step.

Homework Statement



Using the best estimate and uncertainty for the fall time, calculate the value of "g" with the appropriate number of significant figures.

fall time = 0.4249 +/- 0.0001 seconds
height = 1.002 +/- 0.005 meters


Homework Equations



acceleration = height/(time)^2 (?)


The Attempt at a Solution



I'm not even sure where to start...
 
Last edited:
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Use the formula

d = v1*t + (1/2)at^2

apply this formula to this situation...
 
Since in this problem, the object is "falling" (i.e. not thrown up or down), v1= 0. Put in the given values for d and t and you have a single equation to solve for a (for gravity problems, a= v).
 
Thanks to both of you for your help :)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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