NO ME SALEN
SOLVED PHYSICS EXCERCISES FROM THE CBC
Cinemática vectorial
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Aditional No me salen 1.10* - An automovil displaces Northward at 50km/h, then, it displaces Eastward, for 4 hours, travelling 400km in the process. Finally, it heads to the South, at 100km/h for 300km. The average speed modulus is:
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a) 40 km/h
d) 100 km/h
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b) 50 km/h
e) 30 km/h |
c) 0 km/h
f) 25 km/h |
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A really simple excercise that had a very low performance, only a few students could solve this correctly in the exam. Most of the calculations and the general procedure is so easy than you can (and should) solve it mentally
I´ll solve it step by step as I would (almost mentally) have done, being I the student at the exam. |
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The first displacemen, Δr1, to the north, goes for three hours, at 50 km/h. Then, in this first movement, it travels 150 km.
The second displacement, Δr2,was 200km to the East, it lasted for 4 hours.
Finally, the third displacement, Δr3, was 300km to the South, at 100km/h, that means it lasted for 3 hours.
The average total speed, the one we are asked by the excercise, is the quotient between the total displacement, ΔrT, and the time spent in that total displacement.
The total displacement is in green, the vector wich has it´s origin in the origin of the first displacement, and it´s head in the last displacement´s head. It´s just the vectorial sum of the vectors. |
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To know their modulus, you can apply the Pitagoras Theorem in the yellow colored triangle up there.
|ΔrT|² = (200 km)² + (150 km)²
|ΔrT| = 250 km
the total length is the sum of the lengths of each section. The first was 3 h, the second 4 and the last 3. In total, ΔtT, 10 hours. Then:
vm = |ΔrT| / ΔtT
vm = 250 km /10 h
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It was not so grievous
CHALLENGE: express the total average speed in vector notation, according to the reference system adopted in the scheme. |
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| *Excercise taken at the first midterm exam in University city, first quarter 2015. |
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| Some Rights Reserved. Not allowed to be copied without naming either the author or this source material. Those ones not obeying these rules will be sentenced to hard labor in the Antarctica. Translated by Santi Pisci. Last updated ago-15. Buenos Aires, Argentina. |
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