SOLUTION: Hi, I would just like to say thank you for your help in advanced. My question is as follows: The arm of an indrustrial robot starts at a speed Vo and drops 34.8 cm in 4.2

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Question 1002246: Hi,
I would just like to say thank you for your help in advanced.
My question is as follows:
The arm of an indrustrial robot starts at a speed Vo and drops 34.8 cm in 4.28 seconds, at constant acceleration a. Its motion is described by
s= Vot + (at^2)/2
or
34.8 = 4.28Vo + [a(4.28)^2]/2
In another trial the arm is found to drop 58.3 cm in 5.57 seconds, with the same initial speed and acceleration. Find Vo and a.
Thank you

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
The arm of an indrustrial robot starts at a speed Vo and drops 34.8 cm in 4.28 seconds, at constant acceleration a. Its motion is described by
s= (Vo)t + (at^2)/2
or
34.8 = 4.28Vo + [a(4.28)^2]/2
In another trial the arm is found to drop 58.3 cm in 5.57 seconds, with the same initial speed and acceleration. Find Vo and a.

you get s = 34.8 and t = 4.28

formula becomes:

34.8 = 4.28(Vo) + (a*4.28^2)/2

you have another trial where s = 58.3 and t = 5.57

formula becomes:

58.3 = 5.57(Vo) + (a*5.57^2)/2

since Vo and a remain the same in both equations, you have 2 equations that need to be solved simultaneously.

those equations are:

34.8 = 4.28(Vo) + (a*4.28^2)/2
58.3 = 5.57(Vo) + (a*5.57^2)/2

simplify these equations to get:

34.8 = 4.28(Vo) + 9.1592(a)
58.3 = 5.57(Vo) + 15.51245(a)

multiply both sides of the first equation by 5.57 and multiply both sides of the second equation by 4.28 to get:

193.836 = 23.8396(Vo) + 51.016744(a)
249.524 = 23.8396(Vo) + 66.393286

subtract the first equation from the second equation to get:

55.688 = 0 + 15.376542(a)

simplify to get:

55.688 = 15.376542(a)

solve for a to get:

a = 3.621620518

go back to either original equation and solve for Vo to get:

Vo = .3805732134

that's your solution.

substitute those values for a and Vo in both your original equations and you will get:

34.8 = 4.28(.38057342134) + 9.1592(3.621620518) = 34.8
58.3 = 5.57(.38057342134) + 15.51245(3.621620518) = 58.3

your solution is confirmed as good.

your solution is:

Vo = .38057342134
a = 3.621620518

you could also have solved both of these equations graphically.

you would do this as shown below:

the 2 equations are:

34.8 = 4.28(Vo) + (a*4.28^2)/2
58.3 = 5.57(Vo) + (a*5.57^2)/2

solve for Vo in both equations to get:

Vo = (34.8 - (a*4.28^2)/2)/4.28
Vo = (58.3 - (a*5.57^2)/2)/5.57

set y = Vo and set x = a and the equations become:

y = (34.8 - (x*4.28^2)/2)/4.28
y = (58.3 - (x*5.57^2)/2)/5.57

graph both these equations as is and then find the intersection of both equations on the graph.

you will get the following graphical solution:

the intersection point is shown.

x = a
y = Vo

x = 3.622
a = .381

these are the same solutions obtained by formula except they are rounded to 3 decimal digits.