A gymnast jumps vertically upward from a trampoline, as shown in Figure 4.41. The gymnast leaves the
trampoline at a height of 1,3 m and reaches a
maximum height of 5 m. Ignore the effects air
resistance.
a)
b)
Write down the work-energy theorem.
Calculate the initial speed with which the
gymnast leaves the trampoline.​

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Which statements describe the movement of ocean currents around the globe? check all that apply. strong winds force warm water to sink to the ocean floor. the coriolis effect causes warm and cold water to mix. cool dense water sinks to the ocean floor. warm water replaces cool surface water. wind blowing parallel to the shore causes upwelling of cool water.

The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. what is the specific heat ratio? show the math steps .