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while working on a tall communications tower, a worker throws a wrench horizontally at...

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mpumpkin | Salutatorian

Posted October 20, 2013 at 8:40 PM via web

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while working on a tall communications tower, a worker throws a wrench horizontally at a speed of 3.7m/s. what will the vertical velocity of the wrench be in 4.75 s?

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tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

Posted October 20, 2013 at 9:07 PM (Answer #1)

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Contrary to popular belief, the horizontal motion of the wrench makes no difference to it's vertical motion.  The wrench will still fall vertically at the same rate as if it had been dropped.  If we disregard friction with the air, and assume that the wrench didn't hit anything on the way down, it's gravitational acceleration should be 9.8 `m/s^2` .  To find the wrench's vertical velocity at any given time, we multiply that time by the acceleration, and that will give us the downward velocity in m/s.  Using the value in the question: 4.75.  `(9.8m)/(1 s^2) xx (4.75 s)/1=(46.55m)/s` So the wrench will have a downward vertical velocity of 46.55 m/s. 

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tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

Posted October 20, 2013 at 8:59 PM (Answer #1)

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Contrary to popular belief, the horizontal velocity of the wrench has no bearing on the vertical motion of the wrench.  It will accelerate vertically towards the earth at the same rate as if it had been dropped.  The wrench's vertical acceleration, due to gravity is:  `9.8 m/(s^2)` To find the wrench's downward velocity after a given time, assuming it fell with constant acceleration and disregarding resistance from the air, we multiply the acceleration by the elapsed time.  `9.8 xx 4.75=46.55` At 4.75 seconds, the wrench will be falling at 46.55 m/s. 

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