Question 11 (a) A gymnast jumps from a platform at vertical position s, = 1.0m above a trampoline at s, = 0m. The gymnast's vertical velocity at the moment when she leaves the platform (time t = 0) 1s v, = 3.0ms~!. The positive vertical direction is upwards. Assume that the effects of air resistance and friction can be neglected. She touches the trampoline at time = ;. (1) Sketch a graph of the gymnast's vertical position versus time between = 0 and t;. Label s, =0m.t =0, and t; on your graph. (1) Sketch a graph of the gymnast's vertical velocity versus time from the moment she leaves the platform until the moment she touches the trampoline. Label v, = 0ms~!, t =0, and ; on your graph. (111) Calculate the vertical velocity of the gymnast at the instant she touches the trampoline. (1v) The trampoline's canvas is connected to its frame by a number of springs. One of these springs has a spring constant of 2000 Nm". Calculate the strain potential energy of the spring when it is extended by 0.15m from its equilibrium position. Assume that this extension obeys Hooke's Law. (v) The gymnast now does a somersault and rotates with an average angular velocity of 6rads~!. Angular momentum is a conserved quantity and the gymnast had zero angular momentum when she Jumped from the platform. Explain how this 1s possible. (6) A coach standing in the gym hits a drum which emits a sound with a frequency of 110Hz. The speed of sound in air 1s 340 ms1. (1) An athlete 1s running straight towards the coach with velocity 20.0kmh~!. What frequency will the athlete hear? (1) x defines the distance from one edge of the drum's membrane to the opposite edge, passing through the centre of the membrane. A standing wave on the drum membrane can be described by ylx,t) = 24 cos(wt) sin(kx) where y 1s the vertical displacement of the drum's membrane at position r and time . Briefly explain what A, w, and k signify in this equatiorn