An object is released from an aeroplane which is diving at an angle of 30° from the horizontal with a speed of 50m/s. If the plane is at a height of
4000m from the ground when the object is released, find
(a) the velocity of the object when it hits the ground.
(b) the time taken for the object to reach the ground.

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

In a stagnant pool of water, a crayfish may spend much of its time lying with one side of its carapace near the surface of the water. in this position, it will move the walking legs on that side in a rhythmic back-and-forth motion. explain the likely function of this behavior.

Two point charges are on the y axis. a 3.90-µc charge is located at y = 1.25 cm, and a -2.4-µc charge is located at y = −1.80 cm. (a) find the total electric potential at the origin. v (b) find the total electric potential at the point whose coordinates are (1.50 cm, 0). v