A rocket blasts off from the Earth on its way to the moon. As the rocket travels, it loses mass due to burning fuel and ejecting stages of the rocket. When the mass of the rocket has been reduced to one-half of its original mass it has traveled a distance equal to the radius of the Earth away from the surface of the Earth, where it took off. At this point, how does the gravitational force between the rocket and the Earth compare to the gravitational force at lift-off?

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