Consider two cases in which cart a moves to the left with momentum \vec{p}_ip → i and then collides with a second cart which is initially at rest on a horizontal, frictionless air track. in case 1, cart a moves to the left after the collision at a speed of 1 m/s. in case 2, cart a moves to the right after the collision with the same speed as in case 1 (1 m/s). after the collision, the magnitude of the second cart's momentum in case 1 is the magnitude of the second cart's momentum in case 2.

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