An instrument-carrying projectile of mass m1 accidentally explodes at the top of its trajectory. the horizontal distance between launch point and the explosion is x0 . the projectile breaks into two pieces that fly apart horizontally. the larger piece, m3 , has three times the mass of the smaller piece, m2 . to the surprise of the scientist in charge, the smaller piece returns to earth at the launching station. neglect air resistance and effects due to the earth’s curvature. how far away, x3 f , from the original launching point does the larger piece land?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.