Asmall hot-air balloon is filled with 1.02×106 l of air (d = 1.20 g/l). as the air in the balloon is heated, it expands to 1.09×106 l. what is the density of the heated air in the balloon?

The momentum of an isolated system is conserved a) only in inelastic collisions. b) only in elastic collisions. c) in both elastic and inelastic collisions

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

Free runners jump long distances and land on the ground or a wall. how do they apply newton’s second law to lessen the force of impact?