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?

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j