Question

Question 1:

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

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

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

(ii) 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_y = 0 ms^-1,

t = 0, and t₁ on your graph.

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

(iv) The trampoline’s canvas is connected to its frame by a number of springs. One of these springs has a spring constant of 2000 N m^-1 Calculate the strain potential energy of the spring 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 an average angular velocity of 6 rad s^-1.Angular momentum is a conserved quantity and the gymnast had zero angular momentum when she jumped from the platform. Explain how this is possible.

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

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

(ii) 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 byy(x, t) = 2A cos(ωt) sin(kx)

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

Answer 1