A model rocket has the (vertical) velocity vs. time graph shown. The rocket is launched from the ground and flies straight up while its engine fires . We have defined the upward direction to be “positive.” a. Circle the time on the graph when the rocket reaches its HIGHEST ALTITUDE.

b. Calculate the highest altitude it reached in the space below, making your method clear.

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 ?

According to social exchange theory, altruistic behaviors benefit the individual who performs them. t/f

Carbon 14 is a naturally occurring stable