Very far from earth (at r=[infinity]), a spacecraft has run out of fuel and its kinetic energy is zero. if only the gravitational force of the earth were to act on it (i. e., neglect the forces from the sun and other solar system objects), the spacecraft would eventually crash into the earth. the mass of the earth is me and its radius is re. neglect air resistance throughout this problem, since the spacecraft is primarily moving through the near vacuum of space. find the speed se of the spacecraft when it crashes into the earth. express the speed in terms of me, re, and the universal gravitational constant g. now find the spacecraft's speed when its distance from the center of the earth is r=αre, where the coefficient α≥1. express the speed in terms of se and α.

Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue

Which lists the pairs of plates in order from least to greatest in terms of the work done to move the electron?

When electrons are added to the outermost shell of a carbon atom, it forms--an anion that has a larger anion that has a smaller cation that has a larger cation that has a smaller radius.