Q3 was the uniform laminas and you had to find the values for k which made the centre of mass outside the shape. I got k < ⅓ and k>3 for thatcher.
Q6 was the cylinder on the inclined plane. I couldn’t tell you any answers for that because I couldn't do it.
In terms of other questions my answers were:
Q1: Power is 21,000W
M < 66.99
Q2: x = ½, y = - ½, z = 0
v for helium = 900ish
Q3: k>3, k< ⅓
Q4: Velocity of A was something like (u - 2eu)/3
Can’t remember velocity of B.
I couldn’t get my answer for kinetic energy to equal what you were supposed to show.
KE is lowest when e = 1, at this point KE = 0, KE is highest when e=0 and at this point KE = 1/30 (u^2). For one of them they coalesced and moved at u/3. For the other one A moved backwards and B moved forwards.
Q5: Tension is 750N for both
Tension is then around 1020 for one of them and 200 and something for another.
When Jack makes his string 7m, the tensions in the string equal.
Q6: Forces on tie diagram:
5g acting downwards
Reaction perpendicular to plane
Friction parallel to plane.