Enclosed is some guidance algebra.I find this q a little confusing. It quotes "RC" which usually makes me think of electrical circuits and time constants based on converting calculating RC value and equating that to t for one time constant then 2RC for two time constants etc. The theory being that after 5 time constants - 5RC - a circuit is stable. BUT, this q then goes on to mention HALF LIFE. The curves for both half life and time constant are both exponential, as in the number e to the power of something, but the algebra is slightly different. I hope my algebra is ok.
Jill is the input, as she creates the force. The wrench is the output because it gives the force to the finish peace of the chain.
Answer:
a
The height is 
b
The horizontal distance is 
Explanation:
From the question we are told that
The speed is 
The angle is 
The height of the cannon from the ground is h = 2 m
The distance of the net from the ground is k = 1 m
Generally the maximum height she reaches is mathematically represented as
=> ![H = \frac{(15)^2 [sin (40)]^2 }{2 * 9.8} + 2](https://tex.z-dn.net/?f=H%20%20%3D%20%20%5Cfrac%7B%2815%29%5E2%20%5Bsin%20%2840%29%5D%5E2%20%7D%7B2%20%2A%209.8%7D%20%20%2B%20%202)
=>
Generally from kinematic equation
Here s is the displacement which is mathematically represented as
s = [-(h-k)]
=> s = -(2-1)
=> s = -1 m
There reason why s = -1 m is because upward motion canceled the downward motion remaining only the distance of the net from the ground which was covered during the first half but not covered during the second half
a = -g = -9.8
So
=> 
using quadratic formula to solve the equation we have
Generally distance covered along the horizontal is
=> 
=>
Answer:
a. dW = ∫pEsinθdθ b. W = p.E
Explanation:
a. We know torque τ = p × E = pEsinθ where θ is the angle between p and E
Let the torque τ rotate the dipole by an amount dθ. So, the workdone dW = ∫τdθ = ∫pEsinθdθ
b. So, the total work done is gotten by integrating from 90 to θ. So,
W = ∫₉₀⁰dW
= ∫₉₀⁰pEsinθdθ
= pE∫₉₀⁰sinθdθ
= pE(cosθ - cos90)
=pEcosθ
= p.E
