Aparticle of mass m moves in the 2-d potential v=4wy+1 1/(2* +34) with no and 21 positive. (a) find the stable equilibria for the particle. (b) give the lagrangian appropriate for small oscillations about one of the equilibrium positions. (c) give the normal frequencies and modes of vibration corresponding to the equilibrium position in (b).

Aballoon is rising vertically upwards at a velocity of 10m/s. when it is at a height of 45m from the ground, a parachute bails out from it. after 3s he opens his parachute and decelerates ata a constant rate 5m/s.when. (a) what was the height of the parachutist above the ground when he opened his parachute? (b)how far is the parachutist from the balloon at t=3s? (c)with what velocity does the parachutist hit the ground? (d)after how long does the parachutist hit the ground after his exist from the balloon?