An automobile is started from rest with one of its doors initially at right angles. if the hinges of the door are toward the front of the car, the door will slam shut as the automobile picks up speed. obtain a formula for the time needed for the door to close if the acceleration f is constant, the radius of gyration of the door about the axis of rotation is r0, and the center of mass is at a distance a from the hinges. show that if f is 0.3 m/s^2 and the door is a uniform rectangle 1.2m wide, the time will be approximately 3.04 s. show all work.

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