Space probes may be separated from their launchers by exploding bolts. (they bolt away from one another.) suppose a 4800-kg satellite uses this method to separate from the 1500-kg remains of its launcher, and that 5000 j of kinetic energy is supplied to the two parts. what are their subsequent velocities using the frame of reference in which they were at rest before separation?

Suppose you were asked to find the torque about point p due to the normal force n in terms of given quantities. which method of finding the torque would be the easiest to use?

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 of these statements is true? a. quarks pair with leptons to form protons and neutrons. b. quarks pair with bosons to form photons. c. quarks pair with photons to form protons and neutrons. d. quarks pair with other quarks to form protons and neutrons. e. quarks pair with electrons to form protons.