Question 1:

(a) A gymnast jumps from a platform at vertical positions_y = 1.0m above a trampoline at s_y = 0 m. Thegymnast’s vertical velocity at

the moment when she leaves the platform (time t = 0)is  v_y = 3.0 m/s. The positive verticaldirection is upwards. Assume that the effects of air resistance andfriction can be neglected touches the trampoline at time t=t₁

(i) Sketch a graph of the gymnast’s vertical position versustime between t=0 and t1. Label s_y =0m, t=0,andt₁ on your graph.

(ii) Sketch a graph of the gymnast’s vertical velocity versustime from the moment she leaves the platform until the moment shetouches the trampoline. Label v_y = 0ms^-1,

t = 0, and t₁ on your graph.

(iii) Calculate the vertical velocity of the gymnast at theinstant she touches the trampoline.

(iv) The trampoline’s canvas is connected to its frame by anumber of springs. One of these springs has a spring constant of2000 N m^-1 Calculate the strain potential energy of thespring when it is extended by 0.15 m from its equilibrium position.Assume that this extension obeys Hooke’s Law.

(v) The gymnast now does a somersault and rotates with anaverage angular velocity of 6 rad s^-1.Angular momentumis a conserved quantity and the gymnast had zero angular momentumwhen she jumped from the platform. Explain how this is possible.

(b) A coach standing in the gym hits a drum which emits a soundwith a frequency of 110 Hz. The speed of sound in air is 340 m s.

(i) An athlete is running straight towards the coach withvelocity 20.0 km h^-1. What frequency will the athletehear? (3 marks )

(ii) x defines the distance from one edge of the drum’s membraneto the opposite edge, passing through the centre of the membrane. Astanding wave on the drum membrane can be described byy(x, t) = 2Acos(ωt) sin(kx)

where y is the vertical displacement of the drum’s membrane atposition x and time t. Briefly explain what A,ω, and k signify inthis equation.