what would the derivation be for  y= Voy(delta t) - .5g(delta t)2

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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if i wanted to solve for g, what would the derivation be for  y= Voy(delta t) - .5g(delta t)so like i want the equation to be g= ... 

(i understand g is 9.81, but for the purposes of solving for it how would i derive the equation)

Expert Solution
Step 1

here the case is given for an object in free fall motion along the Y axis.

Velocity is defined as the rate of change of displacement, which can be written in calculus as:

v=dsdt

According to equation of kinematics for free fall along Y axis, relation between initial velocity, final velocity and acceleration due to gravity is:

v=v0y-gt

here v is the final velocity after time time t

v0y is the initial velocity

g is the acceleration due to gravity.

 

From above two equations it can be written as:

v0y-gt=dsdt

 

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