Q1. The tendon from Mary's knee extensor muscles attaches to the tibia bone 1.5 in. (4 cm) below the center of her knee joint, and her foot is 15 in. (38 cm) away from her knee joint. What arc length does Mary's foot move through when her knee extensor muscles contract and their point of insertion on the tibia moves through an arc length of 2 in. (5 cm)

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 ?

Abatter hits the baseball a with an initial velocity of v0 = 110 ft/sec directly toward fielder b at an angle of 23° to the horizontal; the initial position of the ball is 2.2 ft above ground level. fielder b requires 0.44 sec to judge where the ball should be caught and begins moving to that position with constant speed. because of great experience, fielder b chooses his running speed so that he arrives at the “catch position” simultaneously with the baseball. the catch position is the field location at which the ball altitude is 8.4 ft. determine the velocity of the ball relative to the fielder at the instant the catch is made.

What is the magnification of a real image if the image is 10.0 cm from a mirror and the object is 50.0 cm from the mirror ? use the equation m=-di/do. a. -5.0 b. 5.0 c. 0.20 d. -0.20