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02quiz_11

# 02quiz_11 - Physics 9A-C Quiz#2 Name key ID(last 4...

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v å h cos å sin å Physics 9A-C Quiz #2 Name: key 4/8/11 ID(last 4): A rock is thrown from the roof of a building with a velocity at an angle å from the horizontal. The building has height h . Ignore air resistance. a) (8 points) Find the speed of the rock just before it hits the ground and show that the speed is independent of the angle å. Solution: a) The speed is the magnitude of the velocity | v | = v x 2 + v y 2 (2 pts) so we need to find the components of the velocity just before is hits the ground. a x = 0 õ v x = cos å = constant. (2 pts) Now find the y -component: We could use v y = sin å - gt, but then we would need to eliminate t . Or a quicker method would be to adapt: v 2 = 2 + 2aÎx to the y -motion õ v y 2 = (vø sin å) 2 - 2 g(-h) (2 pts) Substituting into the speed equation: | v | = v x 2 + v y 2 = v 2 cos 2 α + v 2 sin 2 α + 2 gh (1 pt) Using the identity cos 2 å + sin 2 å = 1 õ | v | = v 2 + 2 gh (1
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