------------------------- I did pictures of the whole problem rather than typing

Question

-------------------------

I did pictures of the whole problem rather than typing it out because I am so lost, I don't even know what parts are important to include for solving this. I have not had algebra or calculus for over 5 years (I'm a grad student) and we have no instruction in this physics lab, so if you have time to post your work, I'd really appreciate seeing it so that I can actually understand it. Thank you in advance!

So far in the lab you dealt with error propagation associated with either addition (subtraction) of two independent variables, or multiplication (division) of two independent variables. Both of those cases are examples of a general formula of function of independent variables x,y,z,etc /(x,y,z, ) then af af ay where ox, Oy, Oz etc. are errors in the measurement of x, y, z respectively. Using the general formula above derive the formula for the error propagation of =x+y if the errors in x and y are or and oy . af ax af ay o2 That answer should look familiar to you. In case of a single variable function /(x) the general formula reduces to df which upon closer inspection makes perfect sense. Consider an arbitrary function of variable x . The "propagation of error" from x to is nothing but the projection of the probable range in x onto probable range in see the picture below how the probable range from ox t + X in x s yproie sont probable range om - to + )

Explanation / Answer

let f = x + y
error in x = dx
error in y = dy
then
df/dx = 1
df/dy = 1
df = sqroot((1*dx)^2 + (1*dy)^2) = sqroot(dx^2 + dy^2)

For range R = vo^2*sin(2*theta)/g
error in theta = d(theta)
then dR/d(theta) = vo^2*2*cos(2*theta)/g
so, dR = (dR/d(theta))*d(theta) = vo^2*2*cos(2*theta)d(theta)/g
dR/R = 2*cot(theta)*d(theta)

so, for d(theta) = 0.5 deg = 0.5*pi/180 rad
vo = 3.9 m/s
theta = 45 deg

dR = (3.9^2/9.81) * 2*cot(45)*0.5*pi/180 = 0.027 m = 2.706 cm

hence, we can see for small 0.5 deg change in angle of projectioon, we can get a range error of 2.7 cm
also, using 45 deg helps us to make all the trigonometric expression become 1 and leaves us to dela with speed

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.