Show work! 1. [5 points] Assume that a ruler is initially suspended such that it

Question

Show work!

1. [5 points] Assume that a ruler is initially suspended such that its lower end is at height, h = 0. The ruler is then dropped and allowed to accelerate (with constant acceleration a = g ), towards the earth. The ruler is caught by a student when it has dropped a distance, d (i.e. the bottom of the ruler is now at the position, d). What is the time t it takes for the ruler to fall a distance d? In other words, use y(t) = yi + vit + 0.5at^2 at and the given initial conditions, to find an expression for t in terms of the distance y. Note: yi = is position at t=0, and vi = velocity at t=0

2. [ 5 points ] Using error propagation, find an expression for the uncertainty in the computed time, t . Express your answer in terms of g and the uncertainty in the distance measurement, d . Assume that g is known precisely (i.e. there is no associated error, g ).

Explanation / Answer

Here ,

initial height , h = 0

yi = 0

distance dropped = d

let the time taken is t

initial speed , vi = 0 m/s

Using second equation of motion

y(t) = vi *t + 0.5 at^2

-d = -0.5 * g *t^2

t = sqrt(2*h/g)

the time taken for the ruler to fall a distance is sqrt(2*h/g)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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