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1. At the end of the first episode of the popular TV series Game of Thrones we see Jamie Lannister, in the name of love, push Bran Stark from a window in one of the towers at Winterfell Castle. Luckily, Bran survives! For the level of injuries he sustained, we can estimate that he hit the ground at a speed of 20 m/s. Assume Bran was pushed from rest and his horizontal velocity is negligible. (a) If we ignore the effects of air resistance, calculate the window height from which Bran was pushed off to achieve such impact speed. (b) Including the effects of aerodynamic drag, Bran Stark's downward acceleration becomes 9.81 -0.02v2 where v is his speed. Recalculate the window height from which Bran was pushed off to achieve such impact speed. Hint: 5{dx = In[x] + c and so dx = In\f(x)] + c (x)