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1- A car, initially going eastward, rounds a 90 degrees curve and ends up heading southward. If the speedometer reading remains constant, what's the direction of the car's average acceleration vector?
2- A plane with airspeed 370 km/h flies perpendicularly across the jet stream, its nose pointed into the jet stream at 32 degree from the perpendicular direction of its flight. Find the speed of the jet stream.
3- An object undergoes acceleration 2.3i + 3.6j m/s^2 for 10 s. At the end of this time, its velocity is 33i + 15j m/s. What was its velocity at the beginning of the 10 s interval? By how much did its speed change? By how much did its direction change? Show that the speed change is not given by the magnitude of the acceleration multiplied by the time. Why not?
4- A particle leaves the origin with initial velocity v0 = 11i + 14j m/s, undergoing constant acceleration a = -1.2i + 0.26j m/s^2. When does the particle cross the y-axis? What's its y-coordinate at the time? How fast is it moving, and in what direction?
5- A jet is diving vertically downward at 1200 km/h. If the pilot can withstand a maximum acceleration of 5g before losing consciousness, at what height must the plane start a quarter turn to pull out of the dive? Assume the speed remains constant.
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In Russia the government actually pays for your education if you do well enough on the entrance exams, so I don't need to pay anything hehe. I guess this is one of the cool things about my country. I was very lucky btw, got the total of 270 out of 300 (90 math, 92 informatics, 88 russian language) on the tests, which was the minimal total mark required to get free education on this speciality.