(a) check all of the following that are correct statements, where e stands for γmc2. read each statement very carefully to make sure that it is exactly correct.
the definition k = e - mc2 is valid even for speeds near the speed of light.
the energy principle can be written esys, f = esys, i + wsurr.
the definition of work is w = fxdeltax + fydeltay + fzdeltaz.
at speeds close to the speed of light, kinetic energy is approximately equal to (1/2)mv2.
the definition of work is w = < fxdeltax, fydeltay, fzdeltaz > .
the definition of work is w = |< fxdeltax, fydeltay, fzdeltaz > |.
the energy principle can be written deltaesys = wsurr.
(b) an object with mass 70 kg moved in outer space. when it was at location < 14, -32, -7 > its speed was 11.5 m/s. a single constant force < 240, 400, -120 > n acted on the object while the object moved to location < 19, -40, -12 > m. what is the speed of the object at this final location?

Abaseball has a mass of 0.145 kg and approaches a bat at 40.0 m/s. after it is hit, the ball leaves the bat at 50.0 m/s directly back. find the impulse of the bat on the ball. 7.25 kg*m/s 13.1 kg*m/s 5.80 kg*m/s 1.45 kg*m/s

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

Choose the most likely outcome of this scenario: jen decided to go bike riding without a helmet. while no one is around during her ride, she is thrown from her bike when her wheel goes into a pothole. she is not injured, but she is terrified to get back on her bike. what happens next? a. her physical health is affected even though she wasn't hurt. b. her mental and emotional health are affected because she is afraid to get back on her bike. c. her social health is affected because she is worried her friends saw the fall. d. her overall health is not affected at all by her fall.